Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of A4×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C22 |
| direct product | A4×D5⋊C16 |
| unambiguous semidirect product | D5⋊(A4×C16) |
| unambiguous semidirect product | (C22×D5⋊C16)⋊C3 |
| derived | C22×C5 ⋊ C2×C3×C16 |
| Hall | C22×D5⋊C16 ⋊ C3 |
| Sylow | C5 ⋊ C2×A4×C16 |
240 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238236);