Show commands:
Magma
magma: G := TransitiveGroup(18, 966);
Group action invariants
| Degree $n$: | $18$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $966$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^9.A_9$ | ||
| 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: | (1,5,7,4,2,6,8,3)(9,18)(10,17)(11,14,15)(12,13,16), (1,18,8,11,9,2,17,7,12,10)(3,4)(5,13,16)(6,14,15) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $181440$: $A_9$ $362880$: 18T888 $46448640$: 18T963 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 6: None
Degree 9: $A_9$
Low degree siblings
36T77856Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 168 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $92897280=2^{15} \cdot 3^{4} \cdot 5 \cdot 7$ | 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: | 92897280.c | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);