Finite Group DatabasebetaFinite Group Databasebeta| order | 18450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×C25×D123 |
| unambiguous semidirect product | C3⋊(C3×C25×D41) |
| Fitting, Hall | C32×C25×C41 ⋊ C2 |
| derived | C3×C41 ⋊ C2×C3×C25 |
| Hall | C25×C41 ⋊ C3×D3 |
| Hall | C32×C41 ⋊ C2×C25 |
| Hall | C32×C25 ⋊ D41 |
| Sylow | C41 ⋊ C3×D3×C25 |
| Sylow | C32 ⋊ C25×D41 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6150 |
4725 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×C25×D41, C3×D25×D123, C3×D75⋊D41, … |
| maximal normal subgroup of | C3×D3×C25×D41, C3×D25×D123, C3×D75⋊D41, … |
| maximal quotient of | C3×C25×Dic123, C2×C3×C25×D123 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18450, 24);