Show commands:
Magma
magma: G := TransitiveGroup(46, 16);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $16$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{23}^2:C_{44}$ | ||
| 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: | (1,12,13,11,15,7,23,14,9,19,22,16,5,4,6,2,10,17,3,8,21,18)(24,32,39,25,30,43,40,46,34,35,33,37,29,45,36,31,41,44,38,27,26,28), (1,41,17,43,14,34,16,40,7,36,13,31,9,42,4,27,15,37,23,38,10,45,11,25,18,46,21,32,19,26,5,30,22,35,3,24,8,39,20,29,12,28,2,44)(6,33) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $4$: $C_4$ $11$: $C_{11}$ $22$: 22T1 $44$: $C_{44}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: None
Low degree siblings
46T16 x 11Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 56 conjugacy class representatives for $C_{23}^2:C_{44}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $23276=2^{2} \cdot 11 \cdot 23^{2}$ | 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: | 23276.d | magma: IdentifyGroup(G);
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| Character table: | 56 x 56 character table |
magma: CharacterTable(G);