Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#74005 |
| Fitting | C3×C5×#380 ⋊ C2 |
| Hall | C3×C5 ⋊ #2315 |
| Sylow | C3 ⋊ C5×#2315 |
1632 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3,4,5)(6,7,8)(18,22)(21,23);(13,14,15,16)(19,24)(21,23);(7,8)(17,19)(18,21)(20,24)(22,23);(9,10,11,12)(14,16)(17,18)(19,23)(20,22)(21,24)360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 48497);