Finite Group DatabasebetaFinite Group Databasebeta| order | 18450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×D225 |
| unambiguous semidirect product | C9⋊(C41×D25) |
| unambiguous semidirect product | C25⋊(D9×C41) |
| Fitting, Hall | C9×C25×C41 ⋊ C2 |
| derived, Hall | C9×C25 ⋊ C2×C41 |
| Hall | C25×C41 ⋊ D9 |
| Hall | C9×C41 ⋊ D25 |
| Sylow | C25 ⋊ D9×C41 |
| Sylow | C9 ⋊ C41×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D225 |
| commutator, cosocle, hypocenter | C9×C25 | C2×C41 |
| Frattini | C3×C5 | D15×C41 |
| Fitting | C9×C25×C41 | C2 |
| socle | C3×C5×C41 | D15 |
| LCS | G ▷ C9×C25 | |
| UCS | C1 ◁ C41 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9225 |
4674 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D41×D225, D9×C41×D25, D225⋊D41, … |
| maximal normal subgroup of | D41×D225, D9×C41×D25, D225⋊D41, … |
| maximal quotient of | C41×Dic225, C2×C41×D225 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18450, 11);