Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C1 |
| direct product | SD16×C7⋊C9 |
| unambiguous semidirect product | (C7×SD16)⋊C9 |
| Hall | C7×SD16 ⋊ C9 |
| Sylow | C7 ⋊ C9×SD16 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 54);