Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4 |
| direct product | C22⋊C4×(C2×D3)⋊C4 |
| Fitting | C2×C3×C4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C22⋊C42 |
4254 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 90968);