Show commands:
Magma
magma: G := TransitiveGroup(44, 48);
Group action invariants
| Degree $n$: | $44$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $48$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{22}^2:C_4$ | ||
| 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: | (3,22)(4,21)(5,19)(6,20)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(23,30)(24,29)(25,28)(26,27)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38), (1,33,8,41)(2,34,7,42)(3,44,5,32)(4,43,6,31)(9,30,22,24)(10,29,21,23)(11,39,19,35)(12,40,20,36)(13,28,17,26)(14,27,18,25)(15,38)(16,37) | 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, $C_2^2$ $8$: $D_{4}$ x 2, $C_4\times C_2$ $16$: $C_2^2:C_4$ $484$: 22T8 $968$: 44T34 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 11: None
Degree 22: 22T8
Low degree siblings
44T48 x 23Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 130 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $1936=2^{4} \cdot 11^{2}$ | 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: | 1936.116 | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);