Finite Group DatabasebetaFinite Group Databasebeta| order | 4032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#10595100 |
| Fitting | C2×C32×C7×D4 ⋊ C22 |
| Hall | C32×C7 ⋊ C2×AGL(1,ℤ/8) |
| Sylow | C32 ⋊ C2×C7×AGL(1,ℤ/8) |
1428 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×#10595100, C7×#11864777, #72246957, … |
| maximal normal subgroup of | D7×#10595100, C7×#11864777, #72246957, … |
Past the SmallGroups library coverage — no SmallGroups id.