Finite Group DatabasebetaFinite Group Databasebeta| order | 18450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C25 · Schur multiplier (H2) = C1 |
| direct product | C9×C25×D41 |
| Fitting, Hall | C9×C25×C41 ⋊ C2 |
| derived, Sylow | C41 ⋊ C2×C9×C25 |
| Hall | C25×C41 ⋊ C2×C9 |
| Hall | C9×C41 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9×C25 | D41 |
| commutator, hypocenter | C41 | C2×C9×C25 |
| Frattini | C3×C5 | C3×C5×D41 |
| Fitting | C9×C25×C41 | C2 |
| socle, cosocle | C3×C5×C41 | C2×C3×C5 |
| prime radical | C3×C5×D41 | C3×C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C9×C25 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9225 |
4950 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C25×#4223, C9×#16861483, C9×D25×D41, … |
| maximal normal subgroup of | C9×C25×#4223, C9×#16861483, C9×D25×D41, … |
| maximal quotient of | C9×C25×Dic41, C2×C9×C25×D41 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18450, 6);