Finite Group DatabasebetaFinite Group Databasebeta| order | 2250 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D25⋊C5 |
| Fitting, Hall | C9×5−1+2 ⋊ C2 |
| derived | C25 ⋊ C2×C5×C9 |
| Sylow | 5−1+2 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D25⋊C5 |
| commutator, hypocenter | C25 | C2×C5×C9 |
| Frattini, socle | C3×C5 | C3×C5×D5 |
| Fitting | C9×5−1+2 | C2 |
| prime radical | C3×D25⋊C5 | C3 |
| cosocle | C3×C25 | C2×C3×C5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C9 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 225 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C9×AGL(1,ℤ/25), 3−1+2×D25⋊C5, D9×D25⋊C5, … |
| maximal normal subgroup of | C9×AGL(1,ℤ/25), 3−1+2×D25⋊C5, D9×D25⋊C5, … |
Past the SmallGroups library coverage — no SmallGroups id.