Show commands:
Magma
magma: G := TransitiveGroup(35, 28);
Group action invariants
| Degree $n$: | $35$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $28$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $A_7$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | yes | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,2,4,8,3,6,12)(5,10,15,19,25,29,22)(7,14,18,24,28,34,9)(11,16,20,27,23,13,17)(21,26,32,35,30,31,33), (2,5,11)(3,7,15)(4,9,10)(6,13,14)(16,21,23)(17,18,22)(19,26,20)(25,30,32)(27,33,34)(28,31,35) | magma: Generators(G);
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Low degree resolvents
noneResolvents shown for degrees $\leq 47$
Subfields
Degree 5: None
Degree 7: None
Low degree siblings
7T6, 15T47 x 2, 21T33, 42T294, 42T299Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
| Label | Cycle Type | Size | Order | Representative |
| $1^{35}$ | $1$ | $1$ | $()$ | |
| $2^{14},1^{7}$ | $105$ | $2$ | $( 2,28)( 5,31)( 6,25)( 8,15)( 9,21)(10,16)(11,29)(12,18)(13,33)(14,27)(19,32) (20,34)(24,35)(26,30)$ | |
| $4^{7},2^{3},1$ | $630$ | $4$ | $( 1, 3)( 2,15,28, 8)( 5,21,31, 9)( 6,18,25,12)( 7,22)(10,34,16,20) (11,32,29,19)(13,26,33,30)(14,35,27,24)(17,23)$ | |
| $3^{11},1^{2}$ | $280$ | $3$ | $( 1,21, 6)( 2,15,26)( 3,18, 5)( 4, 7,22)( 8,33,34)( 9,25,17)(10,30,20) (11,32,19)(12,31,23)(13,28,16)(14,35,24)$ | |
| $7^{5}$ | $360$ | $7$ | $( 1,27,15,29,18, 8,16)( 2, 5,32,14, 6,26,10)( 3,13,35,33, 4,24,17) ( 7,28,11,34,21,12,19)( 9,30,31,25,20,23,22)$ | |
| $7^{5}$ | $360$ | $7$ | $( 1,16, 8,18,29,15,27)( 2,10,26, 6,14,32, 5)( 3,17,24, 4,33,35,13) ( 7,19,12,21,34,11,28)( 9,22,23,20,25,31,30)$ | |
| $5^{7}$ | $504$ | $5$ | $( 1,18,19,14,29)( 2,33, 8,15,16)( 3,21,24,11,27)( 4,30,10,34, 7) ( 5,25, 9,32,23)( 6,31,12,35,17)(13,28,22,26,20)$ | |
| $3^{10},1^{5}$ | $70$ | $3$ | $( 1,17, 5)( 2,22,34)( 3,23, 6)( 4,28,20)( 8,10,26)( 9,35,19)(11,18,27) (12,32,24)(13,15,16)(14,21,29)$ | |
| $6^{4},3^{2},2^{2},1$ | $210$ | $6$ | $( 1, 4,17,28, 5,20)( 2,34,22)( 3, 6,23)( 7,25)( 8,12,10,32,26,24) ( 9,14,35,21,19,29)(11,15,18,16,27,13)(30,33)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $2520=2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ | magma: Order(G);
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| Cyclic: | no | magma: IsCyclic(G);
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| Abelian: | no | magma: IsAbelian(G);
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| Solvable: | no | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 2520.a | magma: IdentifyGroup(G);
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| Character table: |
| Size | |
| 2 P | |
| 3 P | |
| 5 P | |
| 7 P | |
| Type |
magma: CharacterTable(G);