Show commands:
Magma
magma: G := TransitiveGroup(46, 28);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $28$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{22}.C_{23}$ | ||
| 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: | (1,14,26,37,4,16,27,39,6,17,29,42,7,20,31,43,9,22,34,45,12,23,35)(2,13,25,38,3,15,28,40,5,18,30,41,8,19,32,44,10,21,33,46,11,24,36), (1,21,41,16,35,10,30,4,24,44,17,37,12,32,5,25,46,20,39,13,33,7,28)(2,22,42,15,36,9,29,3,23,43,18,38,11,31,6,26,45,19,40,14,34,8,27) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $23$: $C_{23}$ $47104$: 46T19 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $C_{23}$
Low degree siblings
46T28 x 182182Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 182384 conjugacy class representatives for $C_2^{22}.C_{23}$ are not computed
magma: ConjugacyClasses(G);
Group invariants
| Order: | $96468992=2^{22} \cdot 23$ | 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: | 96468992.a | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);