Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C3×D3×#87886 |
| Fitting | C22×C32×C52 ⋊ C23 |
| Hall | C32×C52 ⋊ C22×D4 |
| Sylow | C52 ⋊ C2×C3×D3×D4 |
| Sylow | C32 ⋊ C2×#87886 |
2564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
414 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×#11717375, AGL(1,ℤ/9)×#87886 |
| maximal normal subgroup of | C3×D3×#11717375 |
| maximal quotient of | AGL(1,ℤ/9)×#87886 |
Past the SmallGroups library coverage — no SmallGroups id.