Finite Group DatabasebetaFinite Group Databasebeta| order | 4032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C3×D7×#1004 |
| Fitting | C2×C32×C7×D4 ⋊ C22 |
| Hall | C32×C7 ⋊ C2×H(5,𝔽2) |
| Sylow | C32 ⋊ D7×H(5,𝔽2) |
| Sylow | C7 ⋊ C2×C3×#1004 |
3828 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
405 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×#10596675, C3×D7×#5077, D7×#10591510 |
| maximal normal subgroup of | D7×#10596675, C3×D7×#5077, D7×#10591510 |
Past the SmallGroups library coverage — no SmallGroups id.