Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#68600 |
| Fitting | C3×C5×#336 ⋊ C2 |
| Hall | C3×C5 ⋊ #1749 |
| Sylow | C3 ⋊ C5×#1749 |
824 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)(7,8)(9,11,12,10)(18,21)(22,24);(6,7,8)(14,16)(17,18,19,22,20,21,23,24);(9,10,12,11)(13,14)(15,16)480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 20735);