Show commands:
Magma
magma: G := TransitiveGroup(46, 11);
Group action invariants
Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $11$ | 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: | (1,29,13,46,2,40,14,34,3,28,15,45,4,39,16,33,5,27,17,44,6,38,18,32,7,26,19,43,8,37,20,31,9,25,21,42,10,36,22,30,11,24,23,41,12,35), (1,9,15,8,20,6,7,2,4,17,21)(3,22,19,11,5,12,23,14,13,18,16)(24,40,46,31,34,38,28,30,25,26,35)(27,44,36,33,29,39,37,42,41,32,43) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $22$: $D_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: None
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 64 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $11638=2 \cdot 11 \cdot 23^{2}$ | 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: | 11638.23 | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);