Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D825 |
| unambiguous semidirect product | C3⋊(C11×D275) |
| unambiguous semidirect product | C11⋊(C11×D75) |
| unambiguous semidirect product | C25⋊(C11×D33) |
| Fitting, Hall | C3×C112×C25 ⋊ C2 |
| derived | C3×C11×C25 ⋊ C2×C11 |
| Hall | C112×C25 ⋊ D3 |
| Hall | C3×C112 ⋊ D25 |
| Sylow | C112 ⋊ D75 |
| Hall | C3×C25 ⋊ C11×D11 |
| Sylow | C25 ⋊ C11×D33 |
| Sylow | C3 ⋊ C11×D275 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D825 |
| commutator, cosocle, hypocenter | C3×C11×C25 | C2×C11 |
| Frattini | C5 | C11×D165 |
| Fitting | C3×C112×C25 | C2 |
| socle | C3×C5×C112 | D5 |
| LCS | G ▷ C3×C11×C25 | |
| UCS | C1 ◁ C11 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1650 |
4554 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D11×D75, D11×D825, #49137184, … |
| maximal normal subgroup of | C11×D11×D75, D11×D825, #49137184, … |
| maximal quotient of | C11×Dic825, C2×C11×D825 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 88);