Show commands:
Magma
magma: G := TransitiveGroup(22, 32);
Group action invariants
| Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $32$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{10}.D_{22}$ | ||
| 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: | (1,6)(2,5)(7,22)(8,21)(9,20,10,19)(11,17)(12,18)(13,16)(14,15), (1,4)(2,3)(5,21)(6,22)(7,19,8,20)(9,18,10,17)(11,16,12,15)(13,14) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $22$: $D_{11}$ $44$: $D_{22}$ $22528$: 22T29 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $D_{11}$
Low degree siblings
22T32 x 61, 44T236 x 31, 44T239 x 31, 44T240 x 62, 44T241 x 62, 44T266 x 310, 44T267 x 310, 44T268 x 310, 44T269 x 31, 44T270 x 155, 44T271 x 155, 44T272 x 155, 44T273 x 310, 44T274 x 310, 44T275 x 310Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 200 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $45056=2^{12} \cdot 11$ | 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: | 45056.a | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);