Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D3×#3100 |
| Fitting | C3×#3100 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3100 |
2850 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#60558, D3×#61519 |
| maximal normal subgroup of | D3×#60558, D3×#61519 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1037557);