Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#67570 |
| Fitting | C3×C5×#364 ⋊ C2 |
| Hall | C3×C5 ⋊ #1359 |
| Sylow | C3 ⋊ C5×#1359 |
204 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5)(7,8)(10,14)(11,18)(12,19)(15,17)(16,24)(20,21);(6,7,8)(9,10,11,16,19,14,18,22,13,17,21,24,12,15,20,23)255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 4107);