Show commands:
Magma
magma: G := TransitiveGroup(46, 30);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $30$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{22}.D_{23}$ | ||
| 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: | (1,17)(2,18)(3,15,4,16)(5,13)(6,14)(7,11,8,12)(9,10)(19,45,20,46)(21,43,22,44)(23,42)(24,41)(25,40)(26,39)(27,38,28,37)(29,36)(30,35)(31,33,32,34), (1,29,12,40,22,3,32,14,42,24,6,34,15,44,26,8,36,17,45,28,10,38,19)(2,30,11,39,21,4,31,13,41,23,5,33,16,43,25,7,35,18,46,27,9,37,20) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $46$: $D_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $D_{23}$
Low degree siblings
46T30 x 2046, 46T31 x 2047Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 94,264 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $192937984=2^{23} \cdot 23$ | 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 | ||
| Label: | 192937984.b | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);