Show commands:
Magma
magma: G := TransitiveGroup(46, 35);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $35$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{22}.F_{23}$ | ||
| 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: | (1,18,15,22,3,11,34,14,27,32,19,10,39,42,36,8,46,24,43,29,26,37)(2,17,16,21,4,12,33,13,28,31,20,9,40,41,35,7,45,23,44,30,25,38), (1,26,30,45,18,43,10,11,19,6,42,2,25,29,46,17,44,9,12,20,5,41)(3,34,15,36,24,21,14,28,37,32,8,4,33,16,35,23,22,13,27,38,31,7) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $11$: $C_{11}$ $22$: 22T1 $506$: $F_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $F_{23}$
Low degree siblings
46T36Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 8624 conjugacy class representatives for $C_2^{22}.F_{23}$ are not computed
magma: ConjugacyClasses(G);
Group invariants
| Order: | $2122317824=2^{23} \cdot 11 \cdot 23$ | 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: | yes | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 2122317824.b | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);