Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25×C37 · Schur multiplier (H2) = C1 |
| direct product | C3×D3×C25×C37 |
| unambiguous semidirect product | C3⋊(C2×C3×C25×C37) |
| Fitting, Hall | C32×C25×C37 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C25×C37 |
| Hall | C32×C37 ⋊ C2×C25 |
| Hall | C32×C25 ⋊ C2×C37 |
| Sylow | C32 ⋊ C2×C25×C37 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5550 |
8325 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×C25×D37, C3×D3×C37×D25, C3×D3×D925, … |
| maximal normal subgroup of | C3×D3×C25×D37, C3×D3×C37×D25, C3×D3×D925, … |
| maximal quotient of | C3×Dic3×C25×C37, C2×C3×D3×C25×C37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 29);