Show commands:
Magma
magma: G := TransitiveGroup(46, 24);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $24$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $F_{23}\wr C_2$ | ||
| 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: | (1,9,8,11,2,6,17,7,14,16,10,5,20,21,18,4,23,12,22,15,13,19)(24,32,41,31,37,38,42,35,30,33,45)(25,36,34,26,40,27,44,43,39,46,28), (1,40,11,25,5,34,4,24,23,30,7,31,12,35,9,28,20,46,18,26,10,38)(2,27,15,42,21,33,22,43,3,37,19,36,14,32,17,39,6,44,8,41,16,29)(13,45) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $8$: $D_{4}$ $11$: $C_{11}$ $22$: $D_{11}$, 22T1 x 3 $44$: $D_{22}$, 44T2 $88$: 44T5, 44T6 $242$: 22T7 $484$: 44T27 $968$: 44T33 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 299 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $512072=2^{3} \cdot 11^{2} \cdot 23^{2}$ | 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: | 512072.a | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);