Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C22×D3×#100 |
| Fitting | C22×C3×#100 ⋊ C2 |
| Sylow | C3 ⋊ C23×#100 |
7134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#2002, D3×#13082, C2×D3×#1390, … |
| maximal normal subgroup of | C2×D3×#2002, D3×#13082, C2×D3×#1390, … |
| maximal quotient of | C2×D3×#1783, C2×D3×#1462, C2×D32×#100 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033048);