Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#10621596 |
| Fitting | C23×C32×C7 ⋊ C22 |
| Hall | C32×C7 ⋊ H(5,𝔽2) |
| Sylow | C32 ⋊ #6548 |
| Sylow | C7 ⋊ C3×#1004 |
718 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
243 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D7×#1004, #72246734, #72246772, … |
| maximal normal subgroup of | C3×D7×#1004, #72246734, #72246772, … |
Past the SmallGroups library coverage — no SmallGroups id.