Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C5×#69615 |
| Fitting | C3×C5×#389 ⋊ C2 |
| Hall | C3×C5 ⋊ #1934 |
| Sylow | C3 ⋊ C5×#1934 |
584 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7)(14,16)(17,19,20,18,22,23,21,24);(7,8)(9,11,12,10)(17,18,21,19,22,24,20,23);(9,10,12,11)(13,14)(15,16)(18,23)(19,24)(20,21)360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 30252);