Show commands:
Magma
magma: G := TransitiveGroup(46, 47);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $47$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{23}.A_{23}$ | ||
| 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: | (1,7,14,23,5,18,19,31,26,15,12,34,2,8,13,24,6,17,20,32,25,16,11,33)(3,38,44,9)(4,37,43,10)(21,40,46,30,22,39,45,29)(27,35,28,36), (1,45,11,41,37,22,26,39,16,36,28,34,32,30,20,6,17)(2,46,12,42,38,21,25,40,15,35,27,33,31,29,19,5,18)(3,44,14,9,23)(4,43,13,10,24) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $12926008369442488320000$: $A_{23}$ $25852016738884976640000$: 46T43 $54215608607986106530529280000$: 46T46 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
The 34288 conjugacy class representatives for $C_2^{23}.A_{23}$ are not computed
magma: ConjugacyClasses(G);
Group invariants
| Order: | $108431217215972213061058560000=2^{41} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ | 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: | 108431217215972213061058560000.a | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);