Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C24 |
| direct product | A4×(C2×AGL(1,𝔽5))⋊C4 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊(C4×A4) |
| unambiguous semidirect product | (C22×(C2×AGL(1,𝔽5))⋊C4)⋊C3 |
| Fitting | C23×C4×C5 ⋊ C3×C4 |
| Hall | C22×(C2×AGL(1,𝔽5))⋊C4 ⋊ C3 |
| Sylow | C5 ⋊ A4×#95 |
880 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238261);