Show commands:
Magma
magma: G := TransitiveGroup(22, 37);
Group action invariants
| Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $37$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2\times C_2^{10}.F_{11}$ | ||
| 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: | (1,3,14,19,6)(2,4,13,20,5)(7,11,9,21,16)(8,12,10,22,15)(17,18), (1,11,3,5,22,18,7,16,13,20)(2,12,4,6,21,17,8,15,14,19)(9,10) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $5$: $C_5$ $10$: $C_{10}$ x 3 $20$: 20T3 $110$: $F_{11}$ $220$: 22T6 $112640$: 22T34 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $F_{11}$
Low degree siblings
22T37, 44T333, 44T336, 44T339 x 2, 44T340 x 2, 44T341Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 88 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $225280=2^{12} \cdot 5 \cdot 11$ | 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: | yes | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 225280.a | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);