Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | AGL(1,𝔽5)×#131⋊C3 |
| unambiguous semidirect product | (AGL(1,𝔽5)×#131)⋊C3 |
| Fitting | C5×#131 ⋊ C3×C4 |
| Hall | AGL(1,𝔽5)×#131 ⋊ C3 |
| Sylow | C5 ⋊ C4×#131⋊C3 |
314 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238246);