Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C8 |
| direct product | C5×#71332 |
| Fitting | C3×C5×#498 ⋊ C2 |
| Hall | C3×C5 ⋊ #1705 |
| Sylow | C3 ⋊ C5×#1705 |
428 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 146 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) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8)(17,18,19,21,20,22,23,24);(7,8)(9,10,11,13,12,14,15,16);(7,8)(10,13)(11,15)(14,16)(18,21)(19,23)(22,24)300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 19117);