Show commands:
Magma
magma: G := TransitiveGroup(46, 33);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $(C_2^{22}.C_{23}):C_{11}$ | ||
| 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: | (1,2)(3,10,34,37,8,26,6,17,20,28,14,4,9,33,38,7,25,5,18,19,27,13)(11,42,24,43,32,30,22,36,45,39,16)(12,41,23,44,31,29,21,35,46,40,15), (1,33,35,16,32,9,45,8,19,38,42,2,34,36,15,31,10,46,7,20,37,41)(3,14,5,40,21,17,11,26,23,44,27,4,13,6,39,22,18,12,25,24,43,28) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $11$: $C_{11}$ $253$: $C_{23}:C_{11}$ $518144$: 46T25 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $C_{23}:C_{11}$
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 16,624 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $1061158912=2^{22} \cdot 11 \cdot 23$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | yes | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 1061158912.a | magma: IdentifyGroup(G);
|
| Character table: not available. |
magma: CharacterTable(G);