Show commands:
Magma
magma: G := TransitiveGroup(22, 51);
Group action invariants
| Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $51$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{10}.S_{11}$ | ||
| 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: | (1,14,5,21,11,7,10)(2,13,6,22,12,8,9)(3,19)(4,20)(15,16)(17,18), (1,17,11,3,13,5,16)(2,18,12,4,14,6,15)(7,19,22,10)(8,20,21,9) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $39916800$: $S_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $S_{11}$
Low degree siblings
22T50, 44T1749Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 376 conjugacy class representatives for $C_2^{10}.S_{11}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $40874803200=2^{18} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ | 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: | 40874803200.a | magma: IdentifyGroup(G);
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| Character table: | 376 x 376 character table |
magma: CharacterTable(G);