Show commands:
Magma
magma: G := TransitiveGroup(35, 39);
Group action invariants
| Degree $n$: | $35$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $39$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_7^4:D_5$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | 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: | (1,8,4,11,6,13,2,9,5,12,7,14,3,10)(15,34,18,31,20,30,16,29,19,33,21,32,17,35)(22,28)(23,27)(25,26), (1,17,29,13,25)(2,19,32,10,28)(3,20,34,9,27)(4,16,35,11,22)(5,18,31,14,26)(6,15,30,8,24)(7,21,33,12,23) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $10$: $D_{5}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 5: $D_{5}$
Degree 7: None
Low degree siblings
35T38 x 8, 35T39 x 7Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 316 conjugacy class representatives for $C_7^4:D_5$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $24010=2 \cdot 5 \cdot 7^{4}$ | 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: | yes | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 24010.e | magma: IdentifyGroup(G);
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| Character table: | 316 x 316 character table |
magma: CharacterTable(G);