Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of #3713 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#3713 |
| Hall | C32×C11 ⋊ D8 |
| Sylow | C32 ⋊ C11×D8 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 528 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,19)(17,18)(21,22)(23,24,25);(12,13)(14,16)(15,18)(17,19)(20,21,22)(24,25)231 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 222);