Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of ((C24⋊C5)⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×((C24⋊C5)⋊C2)⋊C3 |
| unambiguous semidirect product | (C4×(C24⋊C5)⋊C2)⋊C3 |
| Fitting | C24×C4 ⋊ C3×D5 |
| derived | C24⋊C5 ⋊ C2×C3×C4 |
| Hall | C4×(C24⋊C5)⋊C2 ⋊ C3 |
186 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | C4×AGL(2,𝔽4), C4×AΓL(1,𝔽16) |
| maximal normal subgroup of | C4×AΓL(1,𝔽16) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239969);