Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1815 |
| unambiguous semidirect product | C3⋊(C5×D605) |
| unambiguous semidirect product | C5⋊(C5×D363) |
| Fitting, Hall | C3×C52×C121 ⋊ C2 |
| derived | C3×C5×C121 ⋊ C2×C5 |
| Hall | C52×C121 ⋊ D3 |
| Hall | C3×C121 ⋊ C5×D5 |
| Sylow | C121 ⋊ C5×D15 |
| Hall | C3×C52 ⋊ D121 |
| Sylow | C52 ⋊ D363 |
| Sylow | C3 ⋊ C5×D605 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1815 |
| commutator, cosocle, hypocenter | C3×C5×C121 | C2×C5 |
| Frattini | C11 | C5×D165 |
| Fitting | C3×C52×C121 | C2 |
| socle | C3×C52×C11 | D11 |
| LCS | G ▷ C3×C5×C121 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3630 |
4545 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D15×D121, C5×D5×D363, C5×D3×D605, … |
| maximal normal subgroup of | C5×D15×D121, C5×D5×D363, C5×D3×D605, … |
| maximal quotient of | C5×Dic1815, C2×C5×D1815 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 36);