Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×#87831 |
| Hall | C52×C9 ⋊ C22⋊C4 |
| Sylow | C52 ⋊ C9×C22⋊C4 |
252 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#11717375, D9×#87831, #72247590, … |
| maximal normal subgroup of | C9×#11717375, D9×#87831, #72247590, … |
Past the SmallGroups library coverage — no SmallGroups id.