Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#2856⋊C3 |
| unambiguous semidirect product | #2856⋊(C3×C5) |
| unambiguous semidirect product | (C5×#2856)⋊C3 |
| Fitting, Hall | C5×#2856 ⋊ C3 |
| Sylow | #2856 ⋊ C3×C5 |
388 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5)(7,9)(10,11,14)(12,18,20)(13,15,19)(16,21,17);(6,7)(8,9)(10,17)(11,18)(12,13)(14,19)(15,16)140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236640);