Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | C2×D4×C7⋊C9 |
| unambiguous semidirect product | C4⋊(C22×C7⋊C9) |
| unambiguous semidirect product | (C2×C7×D4)⋊C9 |
| Hall | C2×C7×D4 ⋊ C9 |
| Sylow | C7 ⋊ C2×D4×C9 |
162 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 504 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2)(8,9,10)(11,13,12)(14,15,17,16,18,20,19,21,22);(3,4,5,6)(7,8,9,11,10,12,13);(4,6)150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 174);