Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of #4323 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×#4323 |
| Fitting | D4×C9×C11 ⋊ C2 |
| Hall | C9×C11 ⋊ D8 |
| Sylow | C11 ⋊ C9×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)(10,11,13,15,17,19,20,18,16,14,12)(22,25)(23,28)(26,27);(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,25)(24,27)(26,28)288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 42);