Show commands:
Magma
magma: G := TransitiveGroup(46, 22);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{23}^2:C_{11}:C_{44}$ | ||
| 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: | (1,45,15,28,21,24,17,42,12,30,23,38,8,25,18,26,19,33,3,36,6,34,4,43,13,37,7,41,11,46,16,35,5,27,20,40,10,39,9,32,2,29,22,31)(14,44), (1,36,7,44,12,43,20,46,19,37,22,41,13,29,17,42,5,26,18,28,2,45,4,40,21,32,16,33,8,30,9,39,6,35,15,24,11,34,23,27,10,25,3,31)(14,38) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $4$: $C_4$ $11$: $C_{11}$ $22$: $D_{11}$, 22T1 $44$: $C_{44}$, 44T3 $242$: 22T7 $484$: 44T26 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: None
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 166 conjugacy class representatives for $C_{23}^2:C_{11}:C_{44}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $256036=2^{2} \cdot 11^{2} \cdot 23^{2}$ | 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: | 256036.a | magma: IdentifyGroup(G);
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| Character table: | 166 x 166 character table |
magma: CharacterTable(G);