Show commands:
Magma
magma: G := TransitiveGroup(24, 24958);
Group action invariants
| Degree $n$: | $24$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $24958$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{11}.A_{12}$ | ||
| 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: | (1,5,13,4,7,9,15,11)(2,6,14,3,8,10,16,12)(17,22,20,23)(18,21,19,24), (1,10,23)(2,9,24)(3,15,8,12,22,5,20,13,18)(4,16,7,11,21,6,19,14,17) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $239500800$: $A_{12}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 4: None
Degree 6: None
Degree 8: None
Degree 12: $A_{12}$
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 325 conjugacy class representatives for $C_2^{11}.A_{12}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $490497638400=2^{20} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 11$ | 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: | 490497638400.a | magma: IdentifyGroup(G);
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| Character table: | 325 x 325 character table |
magma: CharacterTable(G);