Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C4 |
| direct product | C5×#67544 |
| Fitting | C3×C5×#354 ⋊ C2 |
| Hall | C3×C5 ⋊ #1406 |
| Sylow | C3 ⋊ C5×#1406 |
216 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 46 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)(12,21)(15,17)(19,20)(22,23);(6,7,8)(9,10,11,16)(12,15,18,23)(13,17,19,24)(14,20,22,21)135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 5084);