Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23 |
| direct product | C5×#68229 |
| Fitting | C3×C5×Q8⋊C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #1476 |
| Sylow | C3 ⋊ C5×#1476 |
552 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)(17,19,20,24)(18,21,23,22);(7,8)(17,18)(19,21)(20,23)(22,24);(9,10,11,13,12,14,15,16)(17,18,19,21,20,23,24,22)420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 7258);