Show commands:
Magma
magma: G := TransitiveGroup(35, 38);
Group action invariants
| Degree $n$: | $35$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $38$ | 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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| $\card{\Aut(F/K)}$: | $7$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,35,2,31,3,29,6,32,7,34,4,30,5,33)(8,28,12,27,11,24,14,23,13,22,10,26,9,25)(15,19,18,21,20,17,16), (1,7,2,4,3,5,6)(8,35,12,31,11,29,14,32,13,34,10,30,9,33)(15,23,16,26,17,28,20,24,21,22,18,25,19,27) | 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 7, 35T39 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 316 conjugacy classes of elements. Data not shown.
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: not available. |
magma: CharacterTable(G);