Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5×C9 · Schur multiplier (H2) = C23 |
| direct product | C22×C5×D3×C9 |
| unambiguous semidirect product | C3⋊(C23×C5×C9) |
| unambiguous semidirect product | (C2×C3)⋊(C22×C5×C9) |
| Fitting | C22×C3×C5×C9 ⋊ C2 |
| derived | C3 ⋊ C23×C5×C9 |
| Hall | C3×C5×C9 ⋊ C23 |
| Sylow | C3×C9 ⋊ C23×C5 |
212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 349);