Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C29 |
| direct product | C2×#82007 |
| Fitting | C22×C3×M32 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3407 |
2074 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076036);