Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| isoclinism | isoclinic class of D165 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×D165 |
| unambiguous semidirect product | C3⋊(C5×C11×D55) |
| unambiguous semidirect product | C5⋊(C5×C11×D33) |
| Fitting, socle, Hall | C3×C52×C112 ⋊ C2 |
| derived | C3×C5×C11 ⋊ C2×C5×C11 |
| Hall | C52×C112 ⋊ D3 |
| Hall | C3×C112 ⋊ C5×D5 |
| Sylow | C112 ⋊ C5×D15 |
| Hall | C3×C52 ⋊ C11×D11 |
| Sylow | C52 ⋊ C11×D33 |
| Sylow | C3 ⋊ C5×C11×D55 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | D165 |
| commutator, cosocle, hypocenter | C3×C5×C11 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C112 | C2 |
| LCS | G ▷ C3×C5×C11 | |
| UCS | C1 ◁ C5×C11 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
4620 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C11×D11×D15, C5×D11×D165, C5×#20300106, … |
| maximal normal subgroup of | C5×C11×D11×D15, C5×D11×D165, C5×#20300106, … |
| maximal quotient of | C5×C11×Dic165, C2×C5×C11×D165 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 192);