Show commands:
Magma
magma: G := TransitiveGroup(35, 37);
Group action invariants
| Degree $n$: | $35$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $37$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_7^4:C_{10}$ | ||
| 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: | (1,18,31,11,26)(2,17,29,10,24)(3,19,32,12,25)(4,21,33,14,22)(5,16,35,9,27)(6,20,34,13,23)(7,15,30,8,28), (1,28,9,34,16,3,25,10,29,17)(2,23,11,32,18)(4,27,8,33,15,7,26,13,35,20)(5,22,14,30,21,6,24,12,31,19) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $5$: $C_5$ $10$: $C_{10}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 5: $C_5$
Degree 7: None
Low degree siblings
35T37 x 79Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 250 conjugacy class representatives for $C_7^4:C_{10}$
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.d | magma: IdentifyGroup(G);
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| Character table: | 250 x 250 character table |
magma: CharacterTable(G);