Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of AΓL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C2×C5×AΓL(1,𝔽9) |
| unambiguous semidirect product | AGL(1,𝔽9)⋊(C22×C5) |
| unambiguous semidirect product | PSU(3,𝔽2)⋊(C22×C5) |
| Fitting, socle | C2×C32×C5 ⋊ SD16 |
| Hall | C32×C5 ⋊ C2×SD16 |
| Sylow | C32 ⋊ C2×C5×SD16 |
168 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 90 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5885);