Show commands:
Magma
magma: G := TransitiveGroup(35, 33);
Group action invariants
| Degree $n$: | $35$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_7^4:C_5$ | ||
| 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: | (1,26,13,29,19)(2,24,8,32,20)(3,25,14,34,15)(4,22,10,35,18)(5,27,12,31,17)(6,23,9,30,21)(7,28,11,33,16), (1,6,5,3,4,2,7)(8,10,14,12,9,13,11)(15,17,21,19,16,20,18)(29,30,31,34,35,32,33) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $5$: $C_5$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 5: $C_5$
Degree 7: None
Low degree siblings
35T33 x 79Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 485 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $12005=5 \cdot 7^{4}$ | 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: | 12005.16 | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);