Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of Dic36 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D72 |
| Fitting | C8×C9×C11 ⋊ C2 |
| Hall | C9×C11 ⋊ D8 |
| Sylow | C9 ⋊ C11×D8 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 792 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28);(13,19)(14,18)(15,17)(21,28)(22,27)(23,26)(24,25)429 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 51);