Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C5×#71760 |
| Hall | C3×C5 ⋊ #1555 |
| Sylow | C3 ⋊ C5×#1555 |
664 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 170 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) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8)(18,22)(21,23);(10,13)(11,15)(18,21)(19,24)(22,23);(7,8)(9,10,11,14,12,13,15,16)(17,18)(19,21)(20,22)(23,24)270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 10923);