Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of A4×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×A4×#170 |
| unambiguous semidirect product | (C22×C4×#170)⋊C3 |
| derived | C22×C5 ⋊ C3×C4×C8 |
| Hall | C22×C4×#170 ⋊ C3 |
| Sylow | C5 ⋊ C4×C8×A4 |
400 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238255);