Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | D3×D4×#99 |
| Fitting | C3×D4×#99 ⋊ C2 |
| Sylow | C3 ⋊ C2×D4×#99 |
15168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D4×B(4,𝔽2), D3×#6595772, D3×#6533135 |
| maximal normal subgroup of | D3×D4×B(4,𝔽2), D3×#6595772, D3×#6533135 |
Past the SmallGroups library coverage — no SmallGroups id.