Show commands:
Magma
magma: G := TransitiveGroup(44, 32);
Group action invariants
| Degree $n$: | $44$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $32$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $D_4\times F_{11}$ | ||
| 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: | (1,33)(2,34)(3,36)(4,35)(5,30)(6,29)(7,32)(8,31)(9,27)(10,28)(11,25)(12,26)(13,21)(14,22)(15,23)(16,24)(17,18)(37,41)(38,42)(39,43)(40,44), (1,39,5,9,25,4,38,8,11,28)(2,40,6,10,26,3,37,7,12,27)(13,43,21,31,20,16,41,23,29,18)(14,44,22,32,19,15,42,24,30,17)(33,36)(34,35), (1,17,37,31,42,4,20,40,30,44,2,18,38,32,41,3,19,39,29,43)(5,36,13,23,11,8,34,16,22,9,6,35,14,24,12,7,33,15,21,10)(25,28,26,27) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 7 $4$: $C_2^2$ x 7 $5$: $C_5$ $8$: $D_{4}$ x 2, $C_2^3$ $10$: $C_{10}$ x 7 $16$: $D_4\times C_2$ $20$: 20T3 x 7 $40$: 20T12 x 2, 40T7 $80$: 40T20 $110$: $F_{11}$ $220$: 22T6 x 3 $440$: 44T25 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 11: $F_{11}$
Degree 22: 22T6
Low degree siblings
44T32 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 55 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $880=2^{4} \cdot 5 \cdot 11$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | yes | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 880.118 | magma: IdentifyGroup(G);
|
| Character table: not available. |
magma: CharacterTable(G);