Show commands:
Magma
magma: G := TransitiveGroup(46, 42);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $42$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $M_{23}\wr C_2$ | ||
| 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: | (1,46,5,36,2,40,18,33,17,44,19,35,9,24)(3,42,10,30,20,25,14,43,7,29,6,37,13,34)(4,39,22,32,15,27,23,26,21,41,11,31,8,28)(12,38)(16,45), (1,21,4,17,6,15,5,18,10,8,13,2,16,23)(3,20,12,11,7,19,14)(9,22)(24,45,30,35,37,27,43)(25,46,38,40,41,36,42)(26,32,31,28,34,33,29) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ 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 170 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $208119169843200=2^{15} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \cdot 23^{2}$ | 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: | no | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 208119169843200.a | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);