Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×D5×C9⋊C9 |
| unambiguous semidirect product | C5⋊(C22×C9⋊C9) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C9⋊C9) |
| unambiguous semidirect product | (C2×C9×D5)⋊C9 |
| Fitting | C2×C5×C9⋊C9 ⋊ C2 |
| Hall | C5×C9⋊C9 ⋊ C22 |
| Sylow | C5 ⋊ C22×C9⋊C9 |
170 conjugacy classes of subgroups.
| transitive degree | μt(G) = 810 |
264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 168);