Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of AGL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C4×AGL(1,𝔽16) |
| unambiguous semidirect product | (C2×C4×C22⋊A4)⋊C5 |
| unambiguous semidirect product | (C2×C4×C24⋊C5)⋊C3 |
| Fitting, Sylow | C25×C4 ⋊ C3×C5 |
| derived | C24 ⋊ C2×C3×C4×C5 |
| Hall | C2×C4×C24⋊C5 ⋊ C3 |
| Hall | C2×C4×C22⋊A4 ⋊ C5 |
428 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240054);