Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×D9×#1043 |
| Fitting | C22×C52×C9 ⋊ C2×C4 |
| derived, Hall | C52×C9 ⋊ C23×C4 |
| Sylow | C52 ⋊ C22×C4×D9 |
| Sylow | C9 ⋊ C23×#1043 |
2832 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 2832 conjugacy classes of subgroups — too many to draw. Only its 354 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 900 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C22×AGL(1,ℤ/9)×#1043, D9×#11717375 |
| maximal normal subgroup of | C22×AGL(1,ℤ/9)×#1043, D9×#11717375 |
Past the SmallGroups library coverage — no SmallGroups id.