Finite Group DatabasebetaFinite Group Databasebeta| order | 18450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D1025 |
| unambiguous semidirect product | C25⋊(C9×D41) |
| unambiguous semidirect product | C41⋊(C9×D25) |
| Fitting, Hall | C9×C25×C41 ⋊ C2 |
| derived, Hall | C25×C41 ⋊ C2×C9 |
| Hall | C9×C41 ⋊ D25 |
| Hall | C9×C25 ⋊ D41 |
| Sylow | C41 ⋊ C9×D25 |
| Sylow | C25 ⋊ C9×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D1025 |
| commutator, hypocenter | C25×C41 | C2×C9 |
| Frattini | C3×C5 | C3×D205 |
| Fitting | C9×C25×C41 | C2 |
| socle | C3×C5×C41 | C3×D5 |
| prime radical | C3×D1025 | C3 |
| cosocle | C3×C25×C41 | C2×C3 |
| LCS | G ▷ C25×C41 | |
| UCS | C1 ◁ C9 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9225 |
4626 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×#16861480, C9×#16861481, C9×D25×D41, … |
| maximal normal subgroup of | C9×#16861480, C9×#16861481, C9×D25×D41, … |
| maximal quotient of | C9×Dic1025, C2×C9×D1025 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18450, 8);