Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#69130 |
| Fitting | C3×C5×AΣL(1,𝔽16) ⋊ C2 |
| Hall | C3×C5 ⋊ #2196 |
| Sylow | C3 ⋊ C5×#2196 |
708 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2,3,4,5)(8,12)(14,15,16);(7,10)(11,13)(15,16);(6,7)(8,10)(9,11)(12,13)(15,16)165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 42335);