Show commands:
Magma
magma: G := TransitiveGroup(46, 29);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $29$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{22}.C_{46}$ | ||
| 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: | (1,46,43,42,39,38,36,34,32,29,27,26,24,21,19,18,15,14,12,9,7,5,4)(2,45,44,41,40,37,35,33,31,30,28,25,23,22,20,17,16,13,11,10,8,6,3), (1,20,37,9,27,45,18,36,7,26,44,16,33,5,23,41,13,31,4,21,39,12,29,2,19,38,10,28,46,17,35,8,25,43,15,34,6,24,42,14,32,3,22,40,11,30) | 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 x 2 $94208$: 46T20 x 2 $96468992$: 46T28 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $C_{23}$
Low degree siblings
46T29 x 182182Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 364768 conjugacy class representatives for $C_2^{22}.C_{46}$ are not computed
magma: ConjugacyClasses(G);
Group invariants
| Order: | $192937984=2^{23} \cdot 23$ | 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: | 192937984.a | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);