Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D12×#99 |
| Fitting | C3×C4×#99 ⋊ C2 |
| Sylow | C3 ⋊ D4×#99 |
2102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D4×#99, D12×B(4,𝔽2), #72270983, … |
| maximal normal subgroup of | D3×D4×#99, D12×B(4,𝔽2), #72270983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 184893);