Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×D5⋊(C3⋊C8) |
| unambiguous semidirect product | D5⋊(C2×C3×C3⋊C8) |
| derived | C3×C5 ⋊ C22×C3×C8 |
| Hall | C32×C5 ⋊ C22×C8 |
| Sylow | C32 ⋊ C2×D5⋊C8 |
| Sylow | C5 ⋊ C22×C3×C3⋊C8 |
358 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5453);