Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C29 |
| direct product | C2×#79405 |
| Fitting | C2×C3×C8×D4 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2988 |
2434 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1034611);