Show commands:
Magma
magma: G := TransitiveGroup(46, 18);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $18$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $D_{23}^2:C_{22}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,30,7,43,23,24,12,27,21,35,22,41,17,34,19,46,9,32,13,33,16,28)(2,36)(3,42,20,29,4,25,15,45,6,37,5,31,10,38,8,26,18,40,14,39,11,44), (1,10,13,14,22,17,23,2,18,8,20)(4,11,21,9,5,19,16,15,7,12,6)(24,43,29,26,27,42,37,31,33,40,30,41,45,36,39,38,46,28,34,32,25,35) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $8$: $D_{4}$ $11$: $C_{11}$ $22$: 22T1 x 3 $44$: 44T2 $88$: 44T5 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: None
Low degree siblings
46T18Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 64 conjugacy class representatives for $D_{23}^2:C_{22}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $46552=2^{3} \cdot 11 \cdot 23^{2}$ | 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: | 46552.b | magma: IdentifyGroup(G);
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| Character table: | 64 x 64 character table |
magma: CharacterTable(G);