Show commands:
Magma
magma: G := TransitiveGroup(46, 43);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $43$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2.A_{23}$ | ||
| 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: | (1,36,14,39)(2,35,13,40)(3,24,27,12,15,38,42,5,19,8,34,44)(4,23,28,11,16,37,41,6,20,7,33,43)(9,30,31,21,18,26,46)(10,29,32,22,17,25,45), (1,19,33,13,45,18,36,44,16,12,23,5,7,38,25,3,10,27,39,2,20,34,14,46,17,35,43,15,11,24,6,8,37,26,4,9,28,40)(21,41)(22,42)(29,31)(30,32) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $12926008369442488320000$: $A_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: $A_{23}$
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
The 1282 conjugacy class representatives for $C_2.A_{23}$
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.b | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);