Show commands:
Magma
magma: G := TransitiveGroup(46, 41);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $41$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{23}.M_{23}$ | ||
| 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: | (1,39,24,31,34,29,11)(2,40,23,32,33,30,12)(3,42,22,36,26,5,46,44,7,15,17,27,14,20)(4,41,21,35,25,6,45,43,8,16,18,28,13,19)(9,37,10,38), (1,6,22,10,3,42,38,44,39,17,30,2,5,21,9,4,41,37,43,40,18,29)(7,45,20,27,11,34,16,25,13,24,31)(8,46,19,28,12,33,15,26,14,23,32) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $10200960$: $M_{23}$ $20401920$: 46T27 $42785927331840$: 46T40 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $M_{23}$
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 736 conjugacy class representatives for $C_2^{23}.M_{23}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $85571854663680=2^{30} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$ | 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: | no | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 85571854663680.a | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);