Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| direct product | C2×#85857 |
| Fitting | C2×C3×#518 ⋊ C2 |
| Sylow | C3 ⋊ C2×C4×H(5,𝔽2) |
12378 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076168);