Show commands:
Magma
magma: G := TransitiveGroup(46, 23);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $23$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{23}^2:(C_{11}\times D_{22})$ | ||
| 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: | (1,32,5,40,11,29,20,24,22,28,2,34,18,43,19,45,9,25,17,41,6,42)(3,36,8,46,4,38,21,26,12,31,10,27,7,44,14,35,13,33,23,30,15,37)(16,39), (1,10,8,11,18,19,6,14,2,20,16,22,13,15,12,5,4,17,9,21,3,7)(24,33,38,28,25,31,42,43,41,45,37,30,44,39,26,29,46,35,34,36,32,40) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $11$: $C_{11}$ $22$: $D_{11}$, 22T1 x 3 $44$: $D_{22}$, 44T2 $242$: 22T7 $484$: 44T27 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 169 conjugacy class representatives for $C_{23}^2:(C_{11}\times D_{22})$
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.b | magma: IdentifyGroup(G);
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| Character table: | 169 x 169 character table |
magma: CharacterTable(G);