Show commands:
Magma
magma: G := TransitiveGroup(44, 35);
Group action invariants
| Degree $n$: | $44$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $35$ | 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: | (1,29,3,42)(2,30,4,41)(5,32,22,39)(6,31,21,40)(7,44,20,28)(8,43,19,27)(9,34,18,37)(10,33,17,38)(11,24,16,25)(12,23,15,26)(13,36)(14,35), (1,37,17,30)(2,38,18,29)(3,25,15,41)(4,26,16,42)(5,36,14,31)(6,35,13,32)(7,23,11,43)(8,24,12,44)(9,33)(10,34)(19,39,21,28)(20,40,22,27) | 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: $C_2$ x 3
Degree 4: $C_2^2$
Degree 11: None
Degree 22: 22T8
Low degree siblings
44T34 x 6, 44T35 x 5Siblings 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);