Show commands:
Magma
magma: G := TransitiveGroup(46, 13);
Group action invariants
Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $13$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $C_{23}^2:D_{22}$ | ||
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: | (1,39,5,26,9,36,13,46,17,33,21,43,2,30,6,40,10,27,14,37,18,24,22,34,3,44,7,31,11,41,15,28,19,38,23,25,4,35,8,45,12,32,16,42,20,29), (1,23,12,6,9,19,14,5,21,13,17,15,16,4,10,7,20,2,11,18,3,22)(24,40,31,26,36,39,33,45,44,46,42,27,34,43,25,38,35,41,29,30,28,32) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $22$: $D_{11}$ $44$: $D_{22}$ 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
There are 59 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $23276=2^{2} \cdot 11 \cdot 23^{2}$ | 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: | 23276.a | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);