Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#69735 |
| Fitting | C2×C3×C4×C5×C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #1492 |
| Sylow | C3 ⋊ C5×#1492 |
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)(6,7,8)(18,19)(22,23);(7,8)(10,13)(11,16)(14,15)(17,19)(18,21)(20,22)(23,24);(7,8)(9,10)(11,13)(12,15)(14,16)(17,18,20,23,21,19,24,22)540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 8069);