Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#1790⋊C3 |
| unambiguous semidirect product | #1790⋊(C3×C5) |
| unambiguous semidirect product | (C5×#1790)⋊C3 |
| Fitting, Hall | C5×#1790 ⋊ C3 |
| derived | H(5,𝔽2) ⋊ C3×C4×C5 |
| Sylow | #1790 ⋊ C3×C5 |
310 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,3,4,5)(6,7,8,9)(11,16,17,14,15,12);(10,15)(11,17)(12,14)(13,16)160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236383);