Show commands:
Magma
magma: G := TransitiveGroup(24, 5025);
Group action invariants
Degree $n$: | $24$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $5025$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $A_4^2:C_4^2$ | ||
Parity: | $1$ | magma: IsEven(G);
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Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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$\card{\Aut(F/K)}$: | $4$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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Generators: | (1,6,12,3,7,9,2,5,11,4,8,10)(13,23,17,15,22,20,14,24,18,16,21,19), (1,19,12,15)(2,20,11,16)(3,17,9,14)(4,18,10,13)(5,22,6,21)(7,23,8,24) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_4$ x 6, $C_2^2$ $8$: $C_4\times C_2$ x 3 $16$: $C_4^2$ $36$: $C_3^2:C_4$ $72$: 12T40 $144$: 24T240 $576$: $A_4^2:C_4$ $1152$: 12T198 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 3: None
Degree 4: $C_2^2$
Degree 6: $C_3^2:C_4$
Degree 8: None
Degree 12: 12T40
Low degree siblings
24T5025, 32T205470 x 2, 36T3144 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 52 conjugacy class representatives for $A_4^2:C_4^2$
magma: ConjugacyClasses(G);
Group invariants
Order: | $2304=2^{8} \cdot 3^{2}$ | 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: | 2304.gn | magma: IdentifyGroup(G);
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Character table: | 52 x 52 character table |
magma: CharacterTable(G);