Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#70268 |
| Fitting | C2×C3×C5×#103 ⋊ C2 |
| Hall | C3×C5 ⋊ #1872 |
| Sylow | C3 ⋊ C5×#1872 |
808 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)(14,16);(6,7,8)(9,11,12,10)(18,22)(19,20)(23,24);(9,10,12,11)(13,14)(15,16)(17,18,20,22,21,24,19,23)330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 26284);