Show commands:
Magma
magma: G := TransitiveGroup(22, 53);
Group action invariants
| Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $53$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{10}.(C_2\times S_{11})$ | ||
| 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: | (1,12,4,13,2,11,3,14)(5,7,21,19,6,8,22,20)(9,17)(10,18)(15,16), (1,11,5,4,22,17,20,9)(2,12,6,3,21,18,19,10)(7,16,8,15)(13,14), (1,12,4,20,17,14)(2,11,3,19,18,13)(5,15,8,21,6,16,7,22) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $39916800$: $S_{11}$ $79833600$: 22T47 $40874803200$: 22T50 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $S_{11}$
Low degree siblings
22T53, 44T1774, 44T1777 x 2, 44T1778 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 752 conjugacy class representatives for $C_2^{10}.(C_2\times S_{11})$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $81749606400=2^{19} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ | 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: | 81749606400.a | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);