Show commands:
Magma
magma: G := TransitiveGroup(46, 40);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $40$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{22}.M_{23}$ | ||
| 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: | (1,29,38,42,36,2,30,37,41,35)(3,10,39,19,32)(4,9,40,20,31)(5,23,27,7,46,6,24,28,8,45)(11,12)(13,17,21,43,16)(14,18,22,44,15)(25,26), (1,41,25,5,17,20,32,15,33,38,43,22,13,7,36,2,42,26,6,18,19,31,16,34,37,44,21,14,8,35)(3,11,27,45,24)(4,12,28,46,23)(9,29,40,10,30,39) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $10200960$: $M_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $M_{23}$
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 368 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $42785927331840=2^{29} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$ | 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: | no | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 42785927331840.a | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);