Show commands:
Magma
magma: G := TransitiveGroup(46, 7);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $7$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{23}\times D_{23}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $23$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,43,10,32,19,44,5,33,14,45,23,34,9,46,18,35,4,24,13,36,22,25,8,37,17,26,3,38,12,27,21,39,7,28,16,40,2,29,11,41,20,30,6,42,15,31), (1,5,9,13,17,21,2,6,10,14,18,22,3,7,11,15,19,23,4,8,12,16,20)(24,35,46,34,45,33,44,32,43,31,42,30,41,29,40,28,39,27,38,26,37,25,36) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $23$: $C_{23}$ $46$: $D_{23}$, $C_{46}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: None
Low degree siblings
46T7 x 10Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 299 conjugacy class representatives for $C_{23}\times D_{23}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $1058=2 \cdot 23^{2}$ | 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: | 1058.3 | magma: IdentifyGroup(G);
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| Character table: | 299 x 299 character table |
magma: CharacterTable(G);