Show commands:
Magma
magma: G := TransitiveGroup(44, 17);
Group action invariants
| Degree $n$: | $44$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $17$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{11}\times S_4$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $11$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,41,37,33,32,27,24,18,14,9,6,3,44,38,35,29,28,22,19,13,11,7,4,42,39,36,31,25,21,17,16,12,5)(2,43,40,34,30,26,23,20,15,10,8), (1,26,5,32,9,34,14,38,19,43,22,4,25,8,31,12,33,15,37,18,44,23,3,28,7,30,11,36,16,40,17,41,24,2,27,6,29,10,35,13,39,20,42,21) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $6$: $S_3$ $11$: $C_{11}$ $22$: 22T1 $24$: $S_4$ $66$: 33T2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: $S_4$
Degree 11: $C_{11}$
Degree 22: None
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 55 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $264=2^{3} \cdot 3 \cdot 11$ | 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: | 264.31 | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);