Show commands:
Magma
magma: G := TransitiveGroup(46, 46);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{22}.A_{23}$ | ||
| 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: | (1,37,3,25,15)(2,38,4,26,16)(5,18,45,10,40,34,11,7,6,17,46,9,39,33,12,8)(13,14)(19,28,36,43)(20,27,35,44)(21,24,22,23)(29,32,30,31), (1,23,6)(2,24,5)(3,38,45,29,9,42,12,35,31,25,14,18,43,7,33,27,40,19,15)(4,37,46,30,10,41,11,36,32,26,13,17,44,8,34,28,39,20,16) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $12926008369442488320000$: $A_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
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
There are 17,144 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $54215608607986106530529280000=2^{40} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ | 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: | 54215608607986106530529280000.a | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);