Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C4 |
| direct product | C5×#2868⋊C3 |
| unambiguous semidirect product | #2868⋊(C3×C5) |
| unambiguous semidirect product | (C5×#2868)⋊C3 |
| Fitting, Hall | C5×#2868 ⋊ C3 |
| Sylow | #2868 ⋊ C3×C5 |
276 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 276 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) = 25 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,4,5)(6,8,9,13)(7,10,11,12)(14,15,23)(16,22,24)(17,18,19)(20,25,21);(6,7,9,11)(8,12,13,10)(14,16)(15,18)(17,21)(19,24)(23,25)140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236644);