Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#69135 |
| Fitting | C3×C5×AΣL(1,𝔽16) ⋊ C2 |
| Hall | C3×C5 ⋊ #2121 |
| Sylow | C3 ⋊ C5×#2121 |
560 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(7,8)(11,18)(14,22)(17,23)(19,24);(6,7,8)(9,11)(10,14)(12,19)(13,18)(15,17)(16,22)(20,23)(21,24);(9,10)(11,17)(12,20,21,15)(13,16)(14,19,22,24)(18,23)180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 38889);