Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×C9×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C3×C4×C9) |
| Fitting | C2×C3×C5×C9 ⋊ C4 |
| derived, Sylow | C5 ⋊ C2×C3×C4×C9 |
| Hall | C3×C5×C9 ⋊ C2×C4 |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 270 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 315);