Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×C4×D3×M16 |
| Fitting | C2×C3×C4×M16 ⋊ C2 |
| Sylow | C3 ⋊ C22×C4×M16 |
3950 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#60208, C2×D3×#3184, C4×D3×#575, … |
| maximal normal subgroup of | D3×#60208, C2×D3×#3184, C4×D3×#575, … |
| maximal quotient of | C4×D32×M16, C2×D3×#1455 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1032952);