Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C27 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D3×C27 |
| unambiguous semidirect product | C3⋊(C22×C5×C27) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C5×C27) |
| Fitting | C2×C3×C5×C27 ⋊ C2 |
| derived | C3 ⋊ C22×C5×C27 |
| Hall | C3×C5×C27 ⋊ C22 |
| Sylow | C3×C27 ⋊ C22×C5 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 540 |
810 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 180);