Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D3×#1871 |
| Fitting | C3×#1871 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1871 |
2050 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#20902, D3×#23879, D3×#23876 |
| maximal normal subgroup of | D3×#20902, D3×#23879, D3×#23876 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 170738);