Show commands:
Magma
magma: G := TransitiveGroup(46, 31);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $31$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $C_2^{22}.D_{23}$ | ||
| Parity: | $1$ | magma: IsEven(G);
| |
| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
|
| $\card{\Aut(F/K)}$: | $2$ | magma: Order(Centralizer(SymmetricGroup(n), G));
| |
| Generators: | (1,9,17,26,33,42,4,11,19,28,35,44,5,14,21,29,37,45,7,15,24,32,40)(2,10,18,25,34,41,3,12,20,27,36,43,6,13,22,30,38,46,8,16,23,31,39), (1,14,2,13)(3,11)(4,12)(5,10,6,9)(15,46)(16,45)(17,43,18,44)(19,42,20,41)(21,40,22,39)(23,37)(24,38)(25,36)(26,35)(27,33)(28,34)(29,31,30,32) | magma: Generators(G);
|
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 2047, 46T31 x 2046Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 94264 conjugacy class representatives for $C_2^{22}.D_{23}$ are not computed
magma: ConjugacyClasses(G);
Group invariants
| Order: | $192937984=2^{23} \cdot 23$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | yes | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 192937984.b | magma: IdentifyGroup(G);
| |
| Character table: | not computed |
magma: CharacterTable(G);