Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C22×C42 |
| direct product | C4×#4840 |
| Fitting | C3×C4×C4⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ C4×#433 |
970 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 167714);