Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×#82546 |
| Fitting | C2×C3×#518 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2883 |
5338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10827753, #72270361, #72270384, … |
| maximal normal subgroup of | C2×#10827753, #72270361, #72270384, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033037);