Finite Group DatabasebetaFinite Group Databasebeta| order | 4032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C27×C3 |
| direct product | C32×D7×#120 |
| Fitting | C32×C7×#120 ⋊ C2 |
| Hall | C32×C7 ⋊ C2×#120 |
| Sylow | C7 ⋊ C2×C32×#120 |
3972 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
630 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C3⋊D3×#120, C32×#120×AGL(1,𝔽7) |
| maximal normal subgroup of | D7×C3⋊D3×#120, C32×#120×AGL(1,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.