Show commands:
Magma
magma: G := TransitiveGroup(46, 19);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $19$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{11}.C_{23}$ | ||
| 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: | (1,11,21,31,41,5,16,25,35,45,9,19,29,39,4,14,24,34,43,8,18,27,38)(2,12,22,32,42,6,15,26,36,46,10,20,30,40,3,13,23,33,44,7,17,28,37), (1,34,20,5,37,23,10,42,27,14,45,31,18,3,35,21,7,39,25,11,43,29,16)(2,33,19,6,38,24,9,41,28,13,46,32,17,4,36,22,8,40,26,12,44,30,15) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $23$: $C_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $C_{23}$
Low degree siblings
46T19 x 88Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 112 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $47104=2^{11} \cdot 23$ | 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: | 47104.a | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);