Show commands:
Magma
magma: G := TransitiveGroup(46, 20);
Group action invariants
Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $20$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $C_2^{12}:C_{23}$ | ||
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: | (1,3,6,7,10,12,13,15,18,20,22,23,26,28,30,31,34,36,38,39,42,44,45)(2,4,5,8,9,11,14,16,17,19,21,24,25,27,29,32,33,35,37,40,41,43,46), (1,29,12,40,22,3,31,14,42,23,5,34,16,43,25,8,35,18,46,28,9,37,20,2,30,11,39,21,4,32,13,41,24,6,33,15,44,26,7,36,17,45,27,10,38,19) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $23$: $C_{23}$ $46$: $C_{46}$ $47104$: 46T19 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $C_{23}$
Low degree siblings
46T20 x 88Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 224 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $94208=2^{12} \cdot 23$ | 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: | 94208.a | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);