Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of #3672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#3672 |
| Hall | C7×C9 ⋊ SD16 |
| Sylow | C9 ⋊ C7×SD16 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 504 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5,6,7)(8,9,12,14,16,15,10,13,11)(18,21)(19,24)(22,23);(9,11)(10,14)(12,13)(15,16)(17,18,20,23)(19,21,24,22)189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 85);