Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×#78688 |
| Fitting | C22×C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2883 |
5338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | #72270101, C2×#10827755, C2×#10827752, … |
| maximal normal subgroup of | #72270101, C2×#10827755, C2×#10827752, … |
| maximal quotient of | #72271850, #72271858, #72272014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033035);