Show commands:
Magma
magma: G := TransitiveGroup(12, 293);
Group action invariants
Degree $n$: | $12$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $293$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $C_2^6.S_6$ | ||
CHM label: | $[2^{6}]S(6)=2wrS(6)$ | ||
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: | (1,12), (1,3,5,7,9,11)(2,4,6,8,10,12), (1,3)(2,12) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $720$: $S_6$ $1440$: $S_6\times C_2$ $23040$: 30T937 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 4: None
Degree 6: $S_6$
Low degree siblings
12T293 x 3, 24T14632 x 2, 24T14633 x 2, 24T14634 x 2, 40T18563 x 2, 40T18564 x 2, 40T18573 x 2, 40T18579 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 65 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $46080=2^{10} \cdot 3^{2} \cdot 5$ | 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: | 46080.c | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);