Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of AΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×AΓL(1,𝔽16) |
| unambiguous semidirect product | (((C24⋊C5)⋊C2)⋊C3)⋊C4 |
| Fitting, socle | C25 ⋊ ΓL(1,𝔽16) |
| derived | AGL(1,𝔽16) ⋊ C2×C4 |
145 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 145 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 30 |
26 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AΓL(2,𝔽4), D3×AΓL(1,𝔽16), #72277485, … |
| maximal normal subgroup of | C4×AΓL(1,𝔽16) |
| maximal quotient of | D3×AΓL(1,𝔽16), C4×AΓL(1,𝔽16) |
| automorphism group of | C3×C24⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240389);