Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×C9×#170 |
| derived, Sylow | C5 ⋊ C3×C8×C9 |
| Hall | C3×C5×C9 ⋊ C8 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1080 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 64);