Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C22 |
| direct product | C22⋊C4×C7⋊C9 |
| unambiguous semidirect product | (C7×C22⋊C4)⋊C9 |
| Hall | C7×C22⋊C4 ⋊ C9 |
| Sylow | C7 ⋊ C9×C22⋊C4 |
102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 504 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,4,6)(3,5,7,8)(10,11,12)(13,15,14)(16,17,19,18,20,22,21,23,24);(2,5)(6,8)(9,10,11,13,12,14,15)150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 49);