Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C22×D3×#99 |
| Fitting | C22×C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ C23×#99 |
7902 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10991, C2×D3×#2021, C2×D3×#1898, … |
| maximal normal subgroup of | D3×#10991, C2×D3×#2021, C2×D3×#1898, … |
| maximal quotient of | C2×D3×#1898, C2×D3×#1781, C2×D3×#2128, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033027);