Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of Dic30 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×D60 |
| unambiguous semidirect product | C4⋊(C9×D15) |
| Fitting | C3×C4×C5×C9 ⋊ C2 |
| Hall | C3×C5×C9 ⋊ D4 |
| Sylow | C3×C9 ⋊ D20 |
| Sylow | C5 ⋊ C9×D12 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
297 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 208);