LMFDB - Galois group: 35T14

Show commands: Magma

magma: G := TransitiveGroup(35, 14);

Group action invariants

Degree $n$:	$35$	magma: t, n := TransitiveGroupIdentification(G); n;
Transitive number $t$:	$14$	magma: t, n := TransitiveGroupIdentification(G); t;
Group:	$C_{35}:C_{12}$
Parity:	$-1$	magma: IsEven(G);
Primitive:	no	magma: IsPrimitive(G);
magma: NilpotencyClass(G);
$\card{\Aut(F/K)}$:	$1$	magma: Order(Centralizer(SymmetricGroup(n), G));
Generators:	(1,22,9,28,11,32,19,3,21,7,29,13,31,17,4,23,6,27,14,33,16,2,24,8,26,12,34,18)(5,25,10,30,15,35,20), (1,8,16,3,6,18)(2,7,17)(4,10,19,5,9,20)(11,28,21,13,26,23)(12,27,22)(14,30,24,15,29,25)(31,33)(34,35)	magma: Generators(G);

Low degree resolvents

|G/N| Galois groups for stem field(s)
$2$: $C_2$
$3$: $C_3$
$4$: $C_4$
$6$: $C_6$
$12$: $C_{12}$
$20$: $F_5$
$21$: $C_7:C_3$
$42$: $(C_7:C_3) \times C_2$
$60$: $F_5\times C_3$
$84$: 28T13

Resolvents shown for degrees $\leq 47$

\|G/N\|	Galois groups for stem field(s)
$2$:	$C_2$
$3$:	$C_3$
$4$:	$C_4$
$6$:	$C_6$
$12$:	$C_{12}$
$20$:	$F_5$
$21$:	$C_7:C_3$
$42$:	$(C_7:C_3) \times C_2$
$60$:	$F_5\times C_3$
$84$:	28T13

Subfields

Degree 5: $F_5$
Degree 7: $C_7:C_3$

Low degree siblings

There are no siblings with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

Label	Cycle Type	Size	Order	Representative
	$1^{35}$	$1$	$1$	$()$
	$3^{10},1^{5}$	$7$	$3$	$( 6,11,21)( 7,12,22)( 8,13,23)( 9,14,24)(10,15,25)(16,31,26)(17,32,27) (18,33,28)(19,34,29)(20,35,30)$
	$3^{10},1^{5}$	$7$	$3$	$( 6,21,11)( 7,22,12)( 8,23,13)( 9,24,14)(10,25,15)(16,26,31)(17,27,32) (18,28,33)(19,29,34)(20,30,35)$
	$4^{7},1^{7}$	$5$	$4$	$( 2, 3, 5, 4)( 7, 8,10, 9)(12,13,15,14)(17,18,20,19)(22,23,25,24)(27,28,30,29) (32,33,35,34)$
	$12^{2},4,3^{2},1$	$35$	$12$	$( 2, 3, 5, 4)( 6,11,21)( 7,13,25, 9,12,23,10,14,22, 8,15,24)(16,31,26) (17,33,30,19,32,28,20,34,27,18,35,29)$
	$12^{2},4,3^{2},1$	$35$	$12$	$( 2, 3, 5, 4)( 6,21,11)( 7,23,15, 9,22,13,10,24,12, 8,25,14)(16,26,31) (17,28,35,19,27,33,20,29,32,18,30,34)$
	$4^{7},1^{7}$	$5$	$4$	$( 2, 4, 5, 3)( 7, 9,10, 8)(12,14,15,13)(17,19,20,18)(22,24,25,23)(27,29,30,28) (32,34,35,33)$
	$12^{2},4,3^{2},1$	$35$	$12$	$( 2, 4, 5, 3)( 6,11,21)( 7,14,25, 8,12,24,10,13,22, 9,15,23)(16,31,26) (17,34,30,18,32,29,20,33,27,19,35,28)$
	$12^{2},4,3^{2},1$	$35$	$12$	$( 2, 4, 5, 3)( 6,21,11)( 7,24,15, 8,22,14,10,23,12, 9,25,13)(16,26,31) (17,29,35,18,27,34,20,28,32,19,30,33)$
	$2^{14},1^{7}$	$5$	$2$	$( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30) (28,29)(32,35)(33,34)$
	$6^{4},3^{2},2^{2},1$	$35$	$6$	$( 2, 5)( 3, 4)( 6,11,21)( 7,15,22,10,12,25)( 8,14,23, 9,13,24)(16,31,26) (17,35,27,20,32,30)(18,34,28,19,33,29)$
	$6^{4},3^{2},2^{2},1$	$35$	$6$	$( 2, 5)( 3, 4)( 6,21,11)( 7,25,12,10,22,15)( 8,24,13, 9,23,14)(16,26,31) (17,30,32,20,27,35)(18,29,33,19,28,34)$
	$5^{7}$	$4$	$5$	$( 1, 2, 3, 4, 5)( 6, 7, 8, 9,10)(11,12,13,14,15)(16,17,18,19,20) (21,22,23,24,25)(26,27,28,29,30)(31,32,33,34,35)$
	$15^{2},5$	$28$	$15$	$( 1, 2, 3, 4, 5)( 6,12,23, 9,15,21, 7,13,24,10,11,22, 8,14,25)(16,32,28,19,35, 26,17,33,29,20,31,27,18,34,30)$
	$15^{2},5$	$28$	$15$	$( 1, 2, 3, 4, 5)( 6,22,13, 9,25,11, 7,23,14,10,21,12, 8,24,15)(16,27,33,19,30, 31,17,28,34,20,26,32,18,29,35)$
	$7^{5}$	$3$	$7$	$( 1, 6,11,16,21,26,31)( 2, 7,12,17,22,27,32)( 3, 8,13,18,23,28,33) ( 4, 9,14,19,24,29,34)( 5,10,15,20,25,30,35)$
	$28,7$	$15$	$28$	$( 1, 6,11,16,21,26,31)( 2, 8,15,19,22,28,35, 4, 7,13,20,24,27,33, 5, 9,12,18, 25,29,32, 3,10,14,17,23,30,34)$
	$28,7$	$15$	$28$	$( 1, 6,11,16,21,26,31)( 2, 9,15,18,22,29,35, 3, 7,14,20,23,27,34, 5, 8,12,19, 25,28,32, 4,10,13,17,24,30,33)$
	$14^{2},7$	$15$	$14$	$( 1, 6,11,16,21,26,31)( 2,10,12,20,22,30,32, 5, 7,15,17,25,27,35) ( 3, 9,13,19,23,29,33, 4, 8,14,18,24,28,34)$
	$35$	$12$	$35$	$( 1, 7,13,19,25,26,32, 3, 9,15,16,22,28,34, 5, 6,12,18,24,30,31, 2, 8,14,20, 21,27,33, 4,10,11,17,23,29,35)$
	$7^{5}$	$3$	$7$	$( 1,16,31,11,26, 6,21)( 2,17,32,12,27, 7,22)( 3,18,33,13,28, 8,23) ( 4,19,34,14,29, 9,24)( 5,20,35,15,30,10,25)$
	$28,7$	$15$	$28$	$( 1,16,31,11,26, 6,21)( 2,18,35,14,27, 8,25, 4,17,33,15,29, 7,23, 5,19,32,13, 30, 9,22, 3,20,34,12,28,10,24)$
	$28,7$	$15$	$28$	$( 1,16,31,11,26, 6,21)( 2,19,35,13,27, 9,25, 3,17,34,15,28, 7,24, 5,18,32,14, 30, 8,22, 4,20,33,12,29,10,23)$
	$14^{2},7$	$15$	$14$	$( 1,16,31,11,26, 6,21)( 2,20,32,15,27,10,22, 5,17,35,12,30, 7,25) ( 3,19,33,14,28, 9,23, 4,18,34,13,29, 8,24)$
	$35$	$12$	$35$	$( 1,17,33,14,30, 6,22, 3,19,35,11,27, 8,24, 5,16,32,13,29,10,21, 2,18,34,15, 26, 7,23, 4,20,31,12,28, 9,25)$

magma: ConjugacyClasses(G);

Group invariants

Order:	$420=2^{2} \cdot 3 \cdot 5 \cdot 7$	magma: Order(G);
Cyclic:	no	magma: IsCyclic(G);
Abelian:	no	magma: IsAbelian(G);
Solvable:	yes	magma: IsSolvable(G);
Nilpotency class:	not nilpotent
Label:	420.14	magma: IdentifyGroup(G);
Character table:

		1A	2A	3A1	3A-1	4A1	4A-1	5A	6A1	6A-1	7A1	7A-1	12A1	12A-1	12A5	12A-5	14A1	14A-1	15A1	15A-1	28A1	28A-1	28A5	28A-5	35A1	35A-1
	Size	1	5	7	7	5	5	4	35	35	3	3	35	35	35	35	15	15	28	28	15	15	15	15	12	12
	2 P	1A	1A	3A-1	3A1	2A	2A	5A	3A-1	3A1	7A1	7A-1	6A1	6A-1	6A-1	6A1	7A1	7A-1	15A-1	15A1	14A1	14A-1	14A-1	14A1	35A1	35A-1
	3 P	1A	2A	1A	1A	4A-1	4A1	5A	2A	2A	7A-1	7A1	4A-1	4A1	4A-1	4A1	14A-1	14A1	5A	5A	28A-1	28A1	28A-5	28A5	35A-1	35A1
	5 P	1A	2A	3A-1	3A1	4A1	4A-1	1A	6A-1	6A1	7A-1	7A1	12A5	12A-5	12A1	12A-1	14A-1	14A1	3A1	3A-1	28A5	28A-5	28A1	28A-1	7A1	7A-1
	7 P	1A	2A	3A1	3A-1	4A-1	4A1	5A	6A1	6A-1	1A	1A	12A-5	12A5	12A-1	12A1	2A	2A	15A1	15A-1	4A1	4A-1	4A1	4A-1	5A	5A
	Type
420.14.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
420.14.1b	R	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$1$	$1$
420.14.1c1	C	$1$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$1$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$1$	$1$	$1$	$1$	$1$
420.14.1c2	C	$1$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$1$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$1$	$1$	$1$	$1$	$1$
420.14.1d1	C	$1$	$- 1$	$1$	$1$	$- i$	$i$	$1$	$- 1$	$- 1$	$1$	$1$	$- i$	$i$	$- i$	$i$	$- 1$	$- 1$	$1$	$1$	$i$	$- i$	$i$	$- i$	$1$	$1$
420.14.1d2	C	$1$	$- 1$	$1$	$1$	$i$	$- i$	$1$	$- 1$	$- 1$	$1$	$1$	$i$	$- i$	$i$	$- i$	$- 1$	$- 1$	$1$	$1$	$- i$	$i$	$- i$	$i$	$1$	$1$
420.14.1e1	C	$1$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$- 1$	$- 1$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$1$	$- ζ_{3}$	$- ζ_{3}^{- 1}$	$- ζ_{3}^{- 1}$	$- ζ_{3}$	$1$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$- 1$	$- 1$	$- 1$	$- 1$	$1$	$1$
420.14.1e2	C	$1$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$- 1$	$- 1$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$1$	$- ζ_{3}^{- 1}$	$- ζ_{3}$	$- ζ_{3}$	$- ζ_{3}^{- 1}$	$1$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$- 1$	$- 1$	$- 1$	$- 1$	$1$	$1$
420.14.1f1	C	$1$	$- 1$	$- ζ_{12}^{2}$	$ζ_{12}^{4}$	$- ζ_{12}^{3}$	$ζ_{12}^{3}$	$1$	$ζ_{12}^{2}$	$- ζ_{12}^{4}$	$1$	$1$	$ζ_{12}$	$- ζ_{12}^{5}$	$ζ_{12}^{5}$	$- ζ_{12}$	$- 1$	$- 1$	$ζ_{12}^{4}$	$- ζ_{12}^{2}$	$ζ_{12}^{3}$	$- ζ_{12}^{3}$	$ζ_{12}^{3}$	$- ζ_{12}^{3}$	$1$	$1$
420.14.1f2	C	$1$	$- 1$	$ζ_{12}^{4}$	$- ζ_{12}^{2}$	$ζ_{12}^{3}$	$- ζ_{12}^{3}$	$1$	$- ζ_{12}^{4}$	$ζ_{12}^{2}$	$1$	$1$	$- ζ_{12}^{5}$	$ζ_{12}$	$- ζ_{12}$	$ζ_{12}^{5}$	$- 1$	$- 1$	$- ζ_{12}^{2}$	$ζ_{12}^{4}$	$- ζ_{12}^{3}$	$ζ_{12}^{3}$	$- ζ_{12}^{3}$	$ζ_{12}^{3}$	$1$	$1$
420.14.1f3	C	$1$	$- 1$	$- ζ_{12}^{2}$	$ζ_{12}^{4}$	$ζ_{12}^{3}$	$- ζ_{12}^{3}$	$1$	$ζ_{12}^{2}$	$- ζ_{12}^{4}$	$1$	$1$	$- ζ_{12}$	$ζ_{12}^{5}$	$- ζ_{12}^{5}$	$ζ_{12}$	$- 1$	$- 1$	$ζ_{12}^{4}$	$- ζ_{12}^{2}$	$- ζ_{12}^{3}$	$ζ_{12}^{3}$	$- ζ_{12}^{3}$	$ζ_{12}^{3}$	$1$	$1$
420.14.1f4	C	$1$	$- 1$	$ζ_{12}^{4}$	$- ζ_{12}^{2}$	$- ζ_{12}^{3}$	$ζ_{12}^{3}$	$1$	$- ζ_{12}^{4}$	$ζ_{12}^{2}$	$1$	$1$	$ζ_{12}^{5}$	$- ζ_{12}$	$ζ_{12}$	$- ζ_{12}^{5}$	$- 1$	$- 1$	$- ζ_{12}^{2}$	$ζ_{12}^{4}$	$ζ_{12}^{3}$	$- ζ_{12}^{3}$	$ζ_{12}^{3}$	$- ζ_{12}^{3}$	$1$	$1$
420.14.3a1	C	$3$	$3$	$0$	$0$	$3$	$3$	$3$	$0$	$0$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$	$0$	$0$	$0$	$0$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$	$0$	$0$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$
420.14.3a2	C	$3$	$3$	$0$	$0$	$3$	$3$	$3$	$0$	$0$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$	$0$	$0$	$0$	$0$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$	$0$	$0$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$
420.14.3b1	C	$3$	$3$	$0$	$0$	$- 3$	$- 3$	$3$	$0$	$0$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$	$0$	$0$	$0$	$0$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$	$0$	$0$	$ζ_{7}^{- 3} + 1 + ζ_{7} + ζ_{7}^{2}$	$- ζ_{7}^{- 3} - ζ_{7} - ζ_{7}^{2}$	$- ζ_{7}^{- 3} - ζ_{7} - ζ_{7}^{2}$	$ζ_{7}^{- 3} + 1 + ζ_{7} + ζ_{7}^{2}$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$
420.14.3b2	C	$3$	$3$	$0$	$0$	$- 3$	$- 3$	$3$	$0$	$0$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$	$0$	$0$	$0$	$0$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$	$0$	$0$	$- ζ_{7}^{- 3} - ζ_{7} - ζ_{7}^{2}$	$ζ_{7}^{- 3} + 1 + ζ_{7} + ζ_{7}^{2}$	$ζ_{7}^{- 3} + 1 + ζ_{7} + ζ_{7}^{2}$	$- ζ_{7}^{- 3} - ζ_{7} - ζ_{7}^{2}$	$- ζ_{7}^{- 3} - 1 - ζ_{7} - ζ_{7}^{2}$	$ζ_{7}^{- 3} + ζ_{7} + ζ_{7}^{2}$
420.14.3c1	C	$3$	$- 3$	$0$	$0$	$- 3 ζ_{28}^{7}$	$3 ζ_{28}^{7}$	$3$	$0$	$0$	$- 1 + ζ_{28}^{2} - ζ_{28}^{4} - ζ_{28}^{8}$	$- ζ_{28}^{2} + ζ_{28}^{4} + ζ_{28}^{8}$	$0$	$0$	$0$	$0$	$1 - ζ_{28}^{2} + ζ_{28}^{4} + ζ_{28}^{8}$	$ζ_{28}^{2} - ζ_{28}^{4} - ζ_{28}^{8}$	$0$	$0$	$ζ_{28} - ζ_{28}^{7} + ζ_{28}^{9} - ζ_{28}^{11}$	$ζ_{28} + ζ_{28}^{9} - ζ_{28}^{11}$	$- ζ_{28} - ζ_{28}^{9} + ζ_{28}^{11}$	$- ζ_{28} + ζ_{28}^{7} - ζ_{28}^{9} + ζ_{28}^{11}$	$- ζ_{28}^{2} + ζ_{28}^{4} + ζ_{28}^{8}$	$- 1 + ζ_{28}^{2} - ζ_{28}^{4} - ζ_{28}^{8}$
420.14.3c2	C	$3$	$- 3$	$0$	$0$	$3 ζ_{28}^{7}$	$- 3 ζ_{28}^{7}$	$3$	$0$	$0$	$- ζ_{28}^{2} + ζ_{28}^{4} + ζ_{28}^{8}$	$- 1 + ζ_{28}^{2} - ζ_{28}^{4} - ζ_{28}^{8}$	$0$	$0$	$0$	$0$	$ζ_{28}^{2} - ζ_{28}^{4} - ζ_{28}^{8}$	$1 - ζ_{28}^{2} + ζ_{28}^{4} + ζ_{28}^{8}$	$0$	$0$	$ζ_{28} + ζ_{28}^{9} - ζ_{28}^{11}$	$ζ_{28} - ζ_{28}^{7} + ζ_{28}^{9} - ζ_{28}^{11}$	$- ζ_{28} + ζ_{28}^{7} - ζ_{28}^{9} + ζ_{28}^{11}$	$- ζ_{28} - ζ_{28}^{9} + ζ_{28}^{11}$	$- 1 + ζ_{28}^{2} - ζ_{28}^{4} - ζ_{28}^{8}$	$- ζ_{28}^{2} + ζ_{28}^{4} + ζ_{28}^{8}$
420.14.3c3	C	$3$	$- 3$	$0$	$0$	$- 3 ζ_{28}^{7}$	$3 ζ_{28}^{7}$	$3$	$0$	$0$	$- ζ_{28}^{2} + ζ_{28}^{4} + ζ_{28}^{8}$	$- 1 + ζ_{28}^{2} - ζ_{28}^{4} - ζ_{28}^{8}$	$0$	$0$	$0$	$0$	$ζ_{28}^{2} - ζ_{28}^{4} - ζ_{28}^{8}$	$1 - ζ_{28}^{2} + ζ_{28}^{4} + ζ_{28}^{8}$	$0$	$0$	$- ζ_{28} - ζ_{28}^{9} + ζ_{28}^{11}$	$- ζ_{28} + ζ_{28}^{7} - ζ_{28}^{9} + ζ_{28}^{11}$	$ζ_{28} - ζ_{28}^{7} + ζ_{28}^{9} - ζ_{28}^{11}$	$ζ_{28} + ζ_{28}^{9} - ζ_{28}^{11}$	$- 1 + ζ_{28}^{2} - ζ_{28}^{4} - ζ_{28}^{8}$	$- ζ_{28}^{2} + ζ_{28}^{4} + ζ_{28}^{8}$
420.14.3c4	C	$3$	$- 3$	$0$	$0$	$3 ζ_{28}^{7}$	$- 3 ζ_{28}^{7}$	$3$	$0$	$0$	$- 1 + ζ_{28}^{2} - ζ_{28}^{4} - ζ_{28}^{8}$	$- ζ_{28}^{2} + ζ_{28}^{4} + ζ_{28}^{8}$	$0$	$0$	$0$	$0$	$1 - ζ_{28}^{2} + ζ_{28}^{4} + ζ_{28}^{8}$	$ζ_{28}^{2} - ζ_{28}^{4} - ζ_{28}^{8}$	$0$	$0$	$- ζ_{28} + ζ_{28}^{7} - ζ_{28}^{9} + ζ_{28}^{11}$	$- ζ_{28} - ζ_{28}^{9} + ζ_{28}^{11}$	$ζ_{28} + ζ_{28}^{9} - ζ_{28}^{11}$	$ζ_{28} - ζ_{28}^{7} + ζ_{28}^{9} - ζ_{28}^{11}$	$- ζ_{28}^{2} + ζ_{28}^{4} + ζ_{28}^{8}$	$- 1 + ζ_{28}^{2} - ζ_{28}^{4} - ζ_{28}^{8}$
420.14.4a	R	$4$	$0$	$4$	$4$	$0$	$0$	$- 1$	$0$	$0$	$4$	$4$	$0$	$0$	$0$	$0$	$0$	$0$	$- 1$	$- 1$	$0$	$0$	$0$	$0$	$- 1$	$- 1$
420.14.4b1	C	$4$	$0$	$4 ζ_{3}^{- 1}$	$4 ζ_{3}$	$0$	$0$	$- 1$	$0$	$0$	$4$	$4$	$0$	$0$	$0$	$0$	$0$	$0$	$- ζ_{3}$	$- ζ_{3}^{- 1}$	$0$	$0$	$0$	$0$	$- 1$	$- 1$
420.14.4b2	C	$4$	$0$	$4 ζ_{3}$	$4 ζ_{3}^{- 1}$	$0$	$0$	$- 1$	$0$	$0$	$4$	$4$	$0$	$0$	$0$	$0$	$0$	$0$	$- ζ_{3}^{- 1}$	$- ζ_{3}$	$0$	$0$	$0$	$0$	$- 1$	$- 1$
420.14.12a1	C	$12$	$0$	$0$	$0$	$0$	$0$	$- 3$	$0$	$0$	$- 4 ζ_{7}^{- 3} - 4 - 4 ζ_{7} - 4 ζ_{7}^{2}$	$4 ζ_{7}^{- 3} + 4 ζ_{7} + 4 ζ_{7}^{2}$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- ζ_{7}^{- 3} - ζ_{7} - ζ_{7}^{2}$	$ζ_{7}^{- 3} + 1 + ζ_{7} + ζ_{7}^{2}$
420.14.12a2	C	$12$	$0$	$0$	$0$	$0$	$0$	$- 3$	$0$	$0$	$4 ζ_{7}^{- 3} + 4 ζ_{7} + 4 ζ_{7}^{2}$	$- 4 ζ_{7}^{- 3} - 4 - 4 ζ_{7} - 4 ζ_{7}^{2}$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$ζ_{7}^{- 3} + 1 + ζ_{7} + ζ_{7}^{2}$	$- ζ_{7}^{- 3} - ζ_{7} - ζ_{7}^{2}$

magma: CharacterTable(G);

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Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	35T14
Degree	$35$
Order	$420$
Cyclic	no
Abelian	no
Solvable	yes
Primitive	no
$p$-group	no
Group:	$C_{35}:C_{12}$