Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#71293 |
| Fitting | C3×C5×#493 ⋊ C2 |
| Hall | C3×C5 ⋊ #2206 |
| Sylow | C3 ⋊ C5×#2206 |
372 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3,4,5)(7,8)(14,18)(15,22)(16,23)(19,20)(21,27)(24,28)(25,26);(6,7,8)(9,10,11,12);(10,12)(13,14)(15,18)(16,25)(17,21)(19,22)(20,23)(24,27)(26,28)255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 42724);