Show commands:
Magma
magma: G := TransitiveGroup(22, 45);
Group action invariants
| Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $45$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $S_{11}$ | ||
| 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: | (1,22,20,18,4,7,9,11,5,14)(2,21,19,17,3,8,10,12,6,13)(15,16), (1,4,20,12,9,17,5)(2,3,19,11,10,18,6)(7,15,14)(8,16,13) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 11: $S_{11}$
Low degree siblings
11T8Siblings 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 $S_{11}$
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.a | magma: IdentifyGroup(G);
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| Character table: | 56 x 56 character table |
magma: CharacterTable(G);