Show commands:
Magma
magma: G := TransitiveGroup(22, 46);
Group action invariants
| Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2\times A_{11}$ | ||
| 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: | (1,5,13,21,19,18,7,16,9,11,4)(2,6,14,22,20,17,8,15,10,12,3), (1,2)(3,4)(5,15,19,14,11,22,7,17,9,6,16,20,13,12,21,8,18,10) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $19958400$: $A_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 11: $A_{11}$
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
The 62 conjugacy class representatives for $C_2\times A_{11}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $39916800=2^{8} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ | 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: | no | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 39916800.b | magma: IdentifyGroup(G);
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| Character table: | 62 x 62 character table |
magma: CharacterTable(G);