Show commands:
Magma
magma: G := TransitiveGroup(18, 968);
Group action invariants
| Degree $n$: | $18$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $968$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^9.S_9$ | ||
| 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: | (1,17,4,11,13,5,9,16,2,18,3,12,14,6,10,15), (1,8,17,10,5,14,12,4,16,2,7,18,9,6,13,11,3,15) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $362880$: $S_9$ $725760$: 18T913 $92897280$: 18T964 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 6: None
Degree 9: $S_9$
Low degree siblings
18T968, 36T82026, 36T82029 x 2, 36T82030 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 300 conjugacy class representatives for $C_2^9.S_9$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $185794560=2^{16} \cdot 3^{4} \cdot 5 \cdot 7$ | 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: | 185794560.a | magma: IdentifyGroup(G);
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| Character table: | 300 x 300 character table |
magma: CharacterTable(G);