Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
| direct product | D3×#1747 |
| Fitting | C3×#1747 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1747 |
930 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#20788, D3×#20370 |
| maximal normal subgroup of | D3×#20788, D3×#20370 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 167069);