Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×#78986 |
| Fitting | C22×C3×#104 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3018 |
4850 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10826479, C2×D3×#3018 |
| maximal normal subgroup of | C2×#10826479, C2×D3×#3018 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1036198);