Show commands:
Magma
magma: G := TransitiveGroup(22, 30);
Group action invariants
| Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $30$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $C_2^{10}.D_{11}$ | ||
| 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: | (1,22,19,17,15,14,11,10,7,6,4)(2,21,20,18,16,13,12,9,8,5,3), (1,9)(2,10)(3,7)(4,8)(11,22,12,21)(13,20)(14,19)(15,17,16,18) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $22$: $D_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $D_{11}$
Low degree siblings
22T29 x 31, 22T30 x 30, 44T147 x 31, 44T148 x 31, 44T204 x 155, 44T205 x 155, 44T206 x 155, 44T207 x 31, 44T208 x 155, 44T209 x 155, 44T210 x 155, 44T211 x 155Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 100 conjugacy class representatives for $C_2^{10}.D_{11}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $22528=2^{11} \cdot 11$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | yes | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 22528.d | magma: IdentifyGroup(G);
| |
| Character table: | 100 x 100 character table |
magma: CharacterTable(G);