Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #548⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#2341⋊C3 |
| unambiguous semidirect product | #2341⋊(C3×C5) |
| unambiguous semidirect product | (C5×#2341)⋊C3 |
| Fitting, Hall | C5×#2341 ⋊ C3 |
| Sylow | #2341 ⋊ C3×C5 |
474 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 474 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)(11,13)(14,15,16,19)(17,27,24,26,23,29,22,21,25,20,18,28);(6,7,8,9)(10,11)(12,13)(14,25,16,24)(15,29,19,28)(17,18,22,23)(20,21,26,27)350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236597);