Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of #67180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C4⋊(C3⋊D15) |
| unambiguous semidirect product | C4⋊(C3×C3⋊D15) |
| Fitting | C33×C4×C5 ⋊ C2 |
| Hall | C33×C5 ⋊ D4 |
| Sylow | C33 ⋊ D20 |
| Sylow | C5 ⋊ C3×C4⋊(C3⋊D3) |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 471);