Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23 |
| direct product | C2×C9×D5⋊AGL(1,𝔽5) |
| Fitting | C2×C52×C9 ⋊ C2×C4 |
| derived, Sylow | C52 ⋊ C22×C4×C9 |
| Hall | C52×C9 ⋊ C22×C4 |
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D9×D5⋊AGL(1,𝔽5), C9×#11717375, #72247521, … |
| maximal normal subgroup of | C2×D9×D5⋊AGL(1,𝔽5), C9×#11717375, #72247521, … |
| maximal quotient of | C9×#11717375 |
Past the SmallGroups library coverage — no SmallGroups id.