Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | D4×A4×AGL(1,𝔽5) |
| unambiguous semidirect product | (C22×D4×AGL(1,𝔽5))⋊C3 |
| Fitting | C22×C5×D4 ⋊ C3×C4 |
| Hall | C22×D4×AGL(1,𝔽5) ⋊ C3 |
| Sylow | C5 ⋊ C4×D4×A4 |
1156 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 1156 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | A4×AGL(1,𝔽5)×S4, D4×AGL(1,𝔽5)×S4, A4×#11717375, … |
| maximal normal subgroup of | D4×AGL(1,𝔽5)×S4 |
| maximal quotient of | A4×#11717375, AGL(1,𝔽5)×AΣL(1,𝔽64) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240102);