Show commands:
Magma
magma: G := TransitiveGroup(44, 5);
Group action invariants
| Degree $n$: | $44$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $5$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $D_4\times C_{11}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
| |
| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
|
| $\card{\Aut(F/K)}$: | $22$ | magma: Order(Centralizer(SymmetricGroup(n), G));
| |
| Generators: | (1,36,25,15,6,40,30,19,10,44,33,23,14,3,38,27,18,8,42,32,21,12,2,35,26,16,5,39,29,20,9,43,34,24,13,4,37,28,17,7,41,31,22,11), (1,44,41,40,37,36,34,31,29,28,26,24,21,20,18,16,14,12,10,8,6,3)(2,43,42,39,38,35,33,32,30,27,25,23,22,19,17,15,13,11,9,7,5,4) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $8$: $D_{4}$ $11$: $C_{11}$ $22$: 22T1 x 3 $44$: 44T2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 11: $C_{11}$
Degree 22: 22T1
Low degree siblings
44T5Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 55 conjugacy class representatives for $D_4\times C_{11}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $88=2^{3} \cdot 11$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | yes | magma: IsSolvable(G);
| |
| Nilpotency class: | $2$ | ||
| Label: | 88.9 | magma: IdentifyGroup(G);
| |
| Character table: | 55 x 55 character table |
magma: CharacterTable(G);