Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #548⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#2351⋊C3 |
| unambiguous semidirect product | #2351⋊(C3×C5) |
| unambiguous semidirect product | (C5×#2351)⋊C3 |
| Fitting, Hall | C5×#2351 ⋊ C3 |
| Sylow | #2351 ⋊ C3×C5 |
354 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5)(10,11,12,13)(15,19)(17,24,18)(20,29,21,26,28,27)(22,25,23);(6,7,8,9)(11,13)(14,29,16,28)(15,25,19,24)(17,21,22,27)(18,26,23,20)350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236599);