Show commands:
Magma
magma: G := TransitiveGroup(44, 34);
Group action invariants
| Degree $n$: | $44$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $34$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2\times C_{11}^2:C_4$ | ||
| 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: | (1,25,19,28)(2,26,20,27)(3,35,17,39)(4,36,18,40)(5,24,15,30)(6,23,16,29)(7,33,14,42)(8,34,13,41)(9,43,11,31)(10,44,12,32)(21,37,22,38), (1,21,20,17,15,14,12,10,7,5,3,2,22,19,18,16,13,11,9,8,6,4)(23,44,41,39,38,36,33,31,30,28,25,24,43,42,40,37,35,34,32,29,27,26) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_4$ x 2, $C_2^2$ $8$: $C_4\times C_2$ $484$: 22T8 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $C_4$
Degree 11: None
Degree 22: 22T8
Low degree siblings
44T34 x 5, 44T35 x 6Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 68 conjugacy class representatives for $C_2\times C_{11}^2:C_4$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $968=2^{3} \cdot 11^{2}$ | 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: | 968.38 | magma: IdentifyGroup(G);
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| Character table: | 68 x 68 character table |
magma: CharacterTable(G);