Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26 |
| direct product | C5×#73653 |
| Fitting | C3×C4×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #2366 |
| Sylow | C3 ⋊ C5×#2366 |
1664 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 20 points:
(1,2,3,4,5)(6,7,8)(17,19,20,18);(13,14,15,16);(9,11,12,10)(18,19);(7,8)(9,10,12,11)(14,16)(17,18,20,19)450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 55152);