Show commands:
Magma
magma: G := TransitiveGroup(46, 44);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $44$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $S_{23}$ | ||
| 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: | (1,5,26,28,10,40,14,15,32,2,6,25,27,9,39,13,16,31)(3,17,29,8)(4,18,30,7)(11,20,33,37)(12,19,34,38)(21,23,35,46,41,43)(22,24,36,45,42,44), (1,29,18,26,16,19,27,6,11,32,42,36)(2,30,17,25,15,20,28,5,12,31,41,35)(3,39)(4,40)(7,14,23,38,22,46)(8,13,24,37,21,45)(9,44)(10,43) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: $S_{23}$
Low degree siblings
23T7Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 1255 conjugacy class representatives for $S_{23}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $25852016738884976640000=2^{19} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ | 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: | 25852016738884976640000.a | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);