Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
| direct product | C2×#73794 |
| Fitting | C2×C3×C4×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2515 |
2182 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 338883);