Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25×C37 · Schur multiplier (H2) = C1 |
| direct product | D9×C25×C37 |
| unambiguous semidirect product | C9⋊(C2×C25×C37) |
| Fitting, Hall | C9×C25×C37 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C25×C37 |
| Hall | C9×C37 ⋊ C2×C25 |
| Hall | C9×C25 ⋊ C2×C37 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8325 |
5550 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C25×D37, D9×C37×D25, D9×D925, … |
| maximal normal subgroup of | D9×C25×D37, D9×C37×D25, D9×D925, … |
| maximal quotient of | C25×Dic9×C37, C2×D9×C25×C37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 9);