Show commands:
Magma
magma: G := TransitiveGroup(46, 9);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $9$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,26,4,45)(2,40,3,31)(5,36,23,35)(6,27,22,44)(7,41,21,30)(8,32,20,39)(9,46,19,25)(10,37,18,34)(11,28,17,43)(12,42,16,29)(13,33,15,38)(14,24), (1,6,11,16,21,3,8,13,18,23,5,10,15,20,2,7,12,17,22,4,9,14,19)(24,45,43,41,39,37,35,33,31,29,27,25,46,44,42,40,38,36,34,32,30,28,26) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $4$: $C_4$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: None
Low degree siblings
46T9 x 11Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 136 conjugacy class representatives for t46n9
magma: ConjugacyClasses(G);
Group invariants
| Order: | $2116=2^{2} \cdot 23^{2}$ | 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: | 2116.9 | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);