Show commands:
Magma
magma: G := TransitiveGroup(46, 38);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{11}.M_{23}$ | ||
| 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: | (1,18,37)(2,17,38)(3,11,22,4,12,21)(5,7,14,6,8,13)(9,34,35)(10,33,36)(15,44,39)(16,43,40)(19,46,25)(20,45,26)(27,28)(29,30), (1,39,34,17,27,21,36,4,12,10,46,23,41,16,20,44,6,13,8,37,31,25,29)(2,40,33,18,28,22,35,3,11,9,45,24,42,15,19,43,5,14,7,38,32,26,30) | 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
The 60 conjugacy class representatives for $C_2^{11}.M_{23}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $20891566080=2^{18} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$ | 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: | 20891566080.a | magma: IdentifyGroup(G);
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| Character table: | 60 x 60 character table |
magma: CharacterTable(G);