Show commands:
Magma
magma: G := TransitiveGroup(46, 26);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $26$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{12}:C_{23}:C_{11}$ | ||
| 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: | (1,8,44,29,38,40,5,31,3,19,23)(2,7,43,30,37,39,6,32,4,20,24)(11,22,36,28,26,14,34,15,45,42,17,12,21,35,27,25,13,33,16,46,41,18), (1,27,40,41,4,35,25,32,10,13,29,2,28,39,42,3,36,26,31,9,14,30)(5,43,12,21,16,37,34,18,45,19,7)(6,44,11,22,15,38,33,17,46,20,8) | 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 $253$: $C_{23}:C_{11}$ $506$: 46T4 $518144$: 46T25 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $C_{23}:C_{11}$
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 64 conjugacy class representatives for $C_2^{12}:C_{23}:C_{11}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $1036288=2^{12} \cdot 11 \cdot 23$ | 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: | 1036288.a | magma: IdentifyGroup(G);
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| Character table: | 64 x 64 character table |
magma: CharacterTable(G);