Show commands:
Magma
magma: G := TransitiveGroup(44, 38);
Group action invariants
| Degree $n$: | $44$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{11}:D_{44}$ | ||
| 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)(2,4)(5,21)(6,22)(7,20)(8,19)(9,18)(10,17)(11,15)(12,16)(23,29)(24,30)(25,28)(26,27)(31,43)(32,44)(33,41)(34,42)(35,39)(36,40)(37,38), (1,34,21,24,19,35,17,26,15,38,14,28,11,40,10,29,8,41,5,31,3,43,2,33,22,23,20,36,18,25,16,37,13,27,12,39,9,30,7,42,6,32,4,44) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $8$: $D_{4}$ $22$: $D_{11}$ x 2 $44$: $D_{22}$ x 2 $88$: 44T6, $D_{44}$ $484$: 22T9 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 11: None
Degree 22: 22T9
Low degree siblings
44T38 x 9Siblings are shown with degree $\leq 47$
A number field with this Galois group has exactly one arithmetically equivalent field.
Conjugacy classes
There are 95 conjugacy classes of elements. Data not shown.
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: | 968.20 | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);