Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#71077 |
| Hall | C3×C5 ⋊ #2185 |
| Sylow | C3 ⋊ C5×#2185 |
452 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 114 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)(6,7,8)(10,12);(7,8)(13,14,17,20)(15,22,24,28)(16,25,23,19)(18,26,27,21);(9,10)(11,12)(14,18)(15,21)(16,23)(19,28)(20,27)(22,25)(24,26)255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 41756);