Show commands:
Magma
magma: G := TransitiveGroup(44, 26);
Group action invariants
| Degree $n$: | $44$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $26$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{11}:C_{44}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $22$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,3,5,7,9,12,14,15,18,19,21,2,4,6,8,10,11,13,16,17,20,22)(23,33,44,31,42,30,39,28,38,25,35,24,34,43,32,41,29,40,27,37,26,36), (1,38,6,43,9,27,13,33,18,39,22,24,4,29,7,36,11,42,15,25,20,32,2,37,5,44,10,28,14,34,17,40,21,23,3,30,8,35,12,41,16,26,19,31) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $4$: $C_4$ $11$: $C_{11}$ $22$: $D_{11}$, 22T1 $44$: $C_{44}$, 44T3 $242$: 22T7 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $C_4$
Degree 11: None
Degree 22: 22T7
Low degree siblings
44T26 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 154 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $484=2^{2} \cdot 11^{2}$ | 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: | 484.5 | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);