Show commands:
Magma
magma: G := TransitiveGroup(46, 32);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $32$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{22}.D_{46}$ | ||
| 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: | (1,34,2,33)(3,31,4,32)(5,29,6,30)(7,27,8,28)(9,25,10,26)(11,24)(12,23)(13,21,14,22)(15,19,16,20)(35,45)(36,46)(37,44)(38,43)(39,41,40,42), (1,45,43,42,39,38,35,34,32,29,27,26,24,22,20,17,15,14,12,9,8,5,4,2,46,44,41,40,37,36,33,31,30,28,25,23,21,19,18,16,13,11,10,7,6,3) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $46$: $D_{23}$ $92$: $D_{46}$ $192937984$: 46T30 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $D_{23}$
Low degree siblings
46T32 x 4093Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 188528 conjugacy class representatives for $C_2^{22}.D_{46}$ are not computed
magma: ConjugacyClasses(G);
Group invariants
| Order: | $385875968=2^{24} \cdot 23$ | 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: | 385875968.a | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);