Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23 |
| direct product | C5×#69106 |
| Fitting | C3×C5×C22⋊C16 ⋊ C2 |
| Hall | C3×C5 ⋊ #2112 |
| Sylow | C3 ⋊ C5×#2112 |
520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3,4,5)(7,8)(14,18)(19,24)(20,25)(26,28);(6,7,8)(10,12);(9,10)(11,12)(13,14,15,19,16,20,21,26,17,18,22,24,23,25,27,28)480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 38518);