Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×AΓL(1,𝔽16) |
| Fitting | C24×C4 ⋊ ΓL(1,𝔽16) |
| derived | AGL(1,𝔽16) ⋊ C42 |
286 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 60 |
A minimal faithful permutation representation — 2 generators on 20 points:
(5,11,7,12,8,19,15,10)(6,20,18,9,13,14,17,16);(1,2,3,4)(6,16,17,18,19,12,8,15,20,10,7,9,11,13,14)52 conjugacy classes — view the full character table.
| maximal subgroup of | C4×AΓL(2,𝔽4) |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((5,11,7,12,8,19,15,10)(6,20,18,9,13,14,17,16), (1,2,3,4)(6,16,17,18,19,12,8,15,20,10,7,9,11,13,14));