Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | D3×#2129 |
| Fitting | C3×#2129 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2129 |
1230 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
69 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#12780, D3×#12713, D3×#33555 |
| maximal normal subgroup of | D3×#12780, D3×#12713, D3×#33555 |
| maximal quotient of | D3×#12583 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322358);