Show commands:
Magma
magma: G := TransitiveGroup(22, 50);
Group action invariants
| Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $50$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $C_2^{10}.S_{11}$ | ||
| 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: | (3,13,7,22,9,12,17,4,14,8,21,10,11,18)(5,6)(15,20,16,19), (1,4,21,19,7,2,3,22,20,8)(5,17,15,11,6,18,16,12)(9,10) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $39916800$: $S_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $S_{11}$
Low degree siblings
22T51, 44T1749Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 376 conjugacy class representatives for $C_2^{10}.S_{11}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $40874803200=2^{18} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | no | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 40874803200.a | magma: IdentifyGroup(G);
| |
| Character table: | 376 x 376 character table |
magma: CharacterTable(G);