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Properties

Label 46T2
Degree $46$
Order $46$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $D_{23}$

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Show commands: Magma

magma: G := TransitiveGroup(46, 2);
 

Group action invariants

Degree $n$:  $46$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $2$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $D_{23}$
Parity:  $-1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $46$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,4)(2,3)(5,46)(6,45)(7,43)(8,44)(9,41)(10,42)(11,40)(12,39)(13,37)(14,38)(15,35)(16,36)(17,34)(18,33)(19,31)(20,32)(21,29)(22,30)(23,28)(24,27)(25,26), (1,11,21,31,41,6,16,26,35,46,10,20,30,39,3,13,23,34,44,7,18,27,38)(2,12,22,32,42,5,15,25,36,45,9,19,29,40,4,14,24,33,43,8,17,28,37)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: $D_{23}$

Low degree siblings

23T2

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

LabelCycle TypeSizeOrderRepresentative
$1^{46}$ $1$ $1$ $()$
$2^{23}$ $23$ $2$ $( 1, 2)( 3,45)( 4,46)( 5,44)( 6,43)( 7,42)( 8,41)( 9,39)(10,40)(11,37)(12,38) (13,36)(14,35)(15,34)(16,33)(17,31)(18,32)(19,30)(20,29)(21,28)(22,27)(23,25) (24,26)$
$23^{2}$ $2$ $23$ $( 1, 3, 6, 7,10,11,13,16,18,20,21,23,26,27,30,31,34,35,38,39,41,44,46) ( 2, 4, 5, 8, 9,12,14,15,17,19,22,24,25,28,29,32,33,36,37,40,42,43,45)$
$23^{2}$ $2$ $23$ $( 1, 6,10,13,18,21,26,30,34,38,41,46, 3, 7,11,16,20,23,27,31,35,39,44) ( 2, 5, 9,14,17,22,25,29,33,37,42,45, 4, 8,12,15,19,24,28,32,36,40,43)$
$23^{2}$ $2$ $23$ $( 1, 7,13,20,26,31,38,44, 3,10,16,21,27,34,39,46, 6,11,18,23,30,35,41) ( 2, 8,14,19,25,32,37,43, 4, 9,15,22,28,33,40,45, 5,12,17,24,29,36,42)$
$23^{2}$ $2$ $23$ $( 1,10,18,26,34,41, 3,11,20,27,35,44, 6,13,21,30,38,46, 7,16,23,31,39) ( 2, 9,17,25,33,42, 4,12,19,28,36,43, 5,14,22,29,37,45, 8,15,24,32,40)$
$23^{2}$ $2$ $23$ $( 1,11,21,31,41, 6,16,26,35,46,10,20,30,39, 3,13,23,34,44, 7,18,27,38) ( 2,12,22,32,42, 5,15,25,36,45, 9,19,29,40, 4,14,24,33,43, 8,17,28,37)$
$23^{2}$ $2$ $23$ $( 1,13,26,38, 3,16,27,39, 6,18,30,41, 7,20,31,44,10,21,34,46,11,23,35) ( 2,14,25,37, 4,15,28,40, 5,17,29,42, 8,19,32,43, 9,22,33,45,12,24,36)$
$23^{2}$ $2$ $23$ $( 1,16,30,44,11,26,39, 7,21,35, 3,18,31,46,13,27,41,10,23,38, 6,20,34) ( 2,15,29,43,12,25,40, 8,22,36, 4,17,32,45,14,28,42, 9,24,37, 5,19,33)$
$23^{2}$ $2$ $23$ $( 1,18,34, 3,20,35, 6,21,38, 7,23,39,10,26,41,11,27,44,13,30,46,16,31) ( 2,17,33, 4,19,36, 5,22,37, 8,24,40, 9,25,42,12,28,43,14,29,45,15,32)$
$23^{2}$ $2$ $23$ $( 1,20,38,10,27,46,18,35, 7,26,44,16,34, 6,23,41,13,31, 3,21,39,11,30) ( 2,19,37, 9,28,45,17,36, 8,25,43,15,33, 5,24,42,14,32, 4,22,40,12,29)$
$23^{2}$ $2$ $23$ $( 1,21,41,16,35,10,30, 3,23,44,18,38,11,31, 6,26,46,20,39,13,34, 7,27) ( 2,22,42,15,36, 9,29, 4,24,43,17,37,12,32, 5,25,45,19,40,14,33, 8,28)$
$23^{2}$ $2$ $23$ $( 1,23,46,21,44,20,41,18,39,16,38,13,35,11,34,10,31, 7,30, 6,27, 3,26) ( 2,24,45,22,43,19,42,17,40,15,37,14,36,12,33, 9,32, 8,29, 5,28, 4,25)$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $46=2 \cdot 23$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  46.1
magma: IdentifyGroup(G);
 
Character table:

1A 2A 23A1 23A2 23A3 23A4 23A5 23A6 23A7 23A8 23A9 23A10 23A11
Size 1 23 2 2 2 2 2 2 2 2 2 2 2
2 P 1A 1A 23A7 23A2 23A9 23A10 23A1 23A11 23A3 23A5 23A8 23A6 23A4
23 P 1A 2A 23A4 23A11 23A8 23A9 23A6 23A3 23A5 23A7 23A2 23A10 23A1
Type
46.1.1a R 1 1 1 1 1 1 1 1 1 1 1 1 1
46.1.1b R 1 −1 1 1 1 1 1 1 1 1 1 1 1
46.1.2a1 R 2 0 ζ23−11+ζ2311 ζ23−1+ζ23 ζ23−10+ζ2310 ζ23−2+ζ232 ζ23−9+ζ239 ζ23−3+ζ233 ζ23−8+ζ238 ζ23−4+ζ234 ζ23−7+ζ237 ζ23−5+ζ235 ζ23−6+ζ236
46.1.2a2 R 2 0 ζ23−10+ζ2310 ζ23−3+ζ233 ζ23−7+ζ237 ζ23−6+ζ236 ζ23−4+ζ234 ζ23−9+ζ239 ζ23−1+ζ23 ζ23−11+ζ2311 ζ23−2+ζ232 ζ23−8+ζ238 ζ23−5+ζ235
46.1.2a3 R 2 0 ζ23−9+ζ239 ζ23−5+ζ235 ζ23−4+ζ234 ζ23−10+ζ2310 ζ23−1+ζ23 ζ23−8+ζ238 ζ23−6+ζ236 ζ23−3+ζ233 ζ23−11+ζ2311 ζ23−2+ζ232 ζ23−7+ζ237
46.1.2a4 R 2 0 ζ23−8+ζ238 ζ23−7+ζ237 ζ23−1+ζ23 ζ23−9+ζ239 ζ23−6+ζ236 ζ23−2+ζ232 ζ23−10+ζ2310 ζ23−5+ζ235 ζ23−3+ζ233 ζ23−11+ζ2311 ζ23−4+ζ234
46.1.2a5 R 2 0 ζ23−7+ζ237 ζ23−9+ζ239 ζ23−2+ζ232 ζ23−5+ζ235 ζ23−11+ζ2311 ζ23−4+ζ234 ζ23−3+ζ233 ζ23−10+ζ2310 ζ23−6+ζ236 ζ23−1+ζ23 ζ23−8+ζ238
46.1.2a6 R 2 0 ζ23−6+ζ236 ζ23−11+ζ2311 ζ23−5+ζ235 ζ23−1+ζ23 ζ23−7+ζ237 ζ23−10+ζ2310 ζ23−4+ζ234 ζ23−2+ζ232 ζ23−8+ζ238 ζ23−9+ζ239 ζ23−3+ζ233
46.1.2a7 R 2 0 ζ23−5+ζ235 ζ23−10+ζ2310 ζ23−8+ζ238 ζ23−3+ζ233 ζ23−2+ζ232 ζ23−7+ζ237 ζ23−11+ζ2311 ζ23−6+ζ236 ζ23−1+ζ23 ζ23−4+ζ234 ζ23−9+ζ239
46.1.2a8 R 2 0 ζ23−4+ζ234 ζ23−8+ζ238 ζ23−11+ζ2311 ζ23−7+ζ237 ζ23−3+ζ233 ζ23−1+ζ23 ζ23−5+ζ235 ζ23−9+ζ239 ζ23−10+ζ2310 ζ23−6+ζ236 ζ23−2+ζ232
46.1.2a9 R 2 0 ζ23−3+ζ233 ζ23−6+ζ236 ζ23−9+ζ239 ζ23−11+ζ2311 ζ23−8+ζ238 ζ23−5+ζ235 ζ23−2+ζ232 ζ23−1+ζ23 ζ23−4+ζ234 ζ23−7+ζ237 ζ23−10+ζ2310
46.1.2a10 R 2 0 ζ23−2+ζ232 ζ23−4+ζ234 ζ23−6+ζ236 ζ23−8+ζ238 ζ23−10+ζ2310 ζ23−11+ζ2311 ζ23−9+ζ239 ζ23−7+ζ237 ζ23−5+ζ235 ζ23−3+ζ233 ζ23−1+ζ23
46.1.2a11 R 2 0 ζ23−1+ζ23 ζ23−2+ζ232 ζ23−3+ζ233 ζ23−4+ζ234 ζ23−5+ζ235 ζ23−6+ζ236 ζ23−7+ζ237 ζ23−8+ζ238 ζ23−9+ζ239 ζ23−10+ζ2310 ζ23−11+ζ2311

magma: CharacterTable(G);