Show commands:
Magma
magma: G := TransitiveGroup(22, 39);
Group action invariants
| Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $39$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{10}.\PSL(2,11)$ | ||
| 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: | (1,9,12,13,17,2,10,11,14,18)(3,22,19,6,8)(4,21,20,5,7)(15,16), (1,7,6,2,8,5)(3,4)(9,21,18)(10,22,17)(11,15,13,12,16,14)(19,20) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $660$: $\PSL(2,11)$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $\PSL(2,11)$
Low degree siblings
22T39Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 56 conjugacy class representatives for $C_2^{10}.\PSL(2,11)$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $675840=2^{12} \cdot 3 \cdot 5 \cdot 11$ | 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: | 675840.a | magma: IdentifyGroup(G);
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| Character table: | 56 x 56 character table |
magma: CharacterTable(G);