Show commands:
Magma
magma: G := TransitiveGroup(14, 57);
Group action invariants
| Degree $n$: | $14$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $57$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^7.S_7$ | ||
| CHM label: | $[2^{7}]S(7)$ | ||
| 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: | (3,13,5)(6,12,10), (3,5)(10,12), (7,14), (1,3,5,7,9,11,13)(2,4,6,8,10,12,14) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $5040$: $S_7$ $10080$: $S_7\times C_2$ $322560$: 14T54 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 7: $S_7$
Low degree siblings
14T57, 28T1097 x 2, 28T1098, 28T1099 x 2, 42T1778 x 2, 42T1779 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 110 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $645120=2^{11} \cdot 3^{2} \cdot 5 \cdot 7$ | 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: | 645120.a | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);