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Magma
magma: G := TransitiveGroup(46, 37);
Group invariants
| Abstract group: | $C_2^{22}.C_{46}.C_{22}$ | magma: IdentifyGroup(G);
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| Order: | $4244635648=2^{24} \cdot 11 \cdot 23$ | 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: | yes | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | magma: NilpotencyClass(G);
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Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $37$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
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| $\card{\Aut(F/K)}$: | $2$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | $(1,17,19,25,43,6,30,10,42,45,11,2,18,20,26,44,5,29,9,41,46,12)(3,24,37,33,21,31,16,13,7,35,27)(4,23,38,34,22,32,15,14,8,36,28)$, $(1,10,2,9)(3,7,4,8)(5,6)(11,46)(12,45)(13,43)(14,44)(15,41)(16,42)(17,40)(18,39)(19,37)(20,38)(21,36,22,35)(23,34,24,33)(25,32,26,31)(27,29,28,30)$ | magma: Generators(G);
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $11$: $C_{11}$ $22$: 22T1 x 3 $44$: 44T2 $506$: $F_{23}$ $1012$: 46T6 $2122317824$: 46T35 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $F_{23}$
Low degree siblings
46T37Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
Conjugacy classes not computedmagma: ConjugacyClasses(G);
Character table
Character table not computed
magma: CharacterTable(G);
Regular extensions
Data not computed