Show commands:
Magma
magma: G := TransitiveGroup(44, 36);
Group action invariants
| Degree $n$: | $44$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $36$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{22}.D_{22}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $2$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,26,12,41,21,35,9,29,19,24,7,40,17,34,6,28,15,44,4,37,14,32,2,25,11,42,22,36,10,30,20,23,8,39,18,33,5,27,16,43,3,38,13,31), (1,14)(2,13)(3,11)(4,12)(5,10)(6,9)(15,21)(16,22)(17,19)(18,20)(23,25)(24,26)(27,44)(28,43)(29,41)(30,42)(31,40)(32,39)(33,37)(34,38) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_4$ x 2, $C_2^2$ $8$: $C_4\times C_2$ $22$: $D_{11}$ x 2 $44$: $D_{22}$ x 2 $88$: 44T7 x 2 $484$: 22T9 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $C_4$
Degree 11: None
Degree 22: 22T9
Low degree siblings
44T36 x 9Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 98 conjugacy class representatives for $C_{22}.D_{22}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $968=2^{3} \cdot 11^{2}$ | 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: | 968.18 | magma: IdentifyGroup(G);
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| Character table: | 98 x 98 character table |
magma: CharacterTable(G);