Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#70977 |
| Fitting | C3×C5×#450 ⋊ C2 |
| Hall | C3×C5 ⋊ #1600 |
| Sylow | C3 ⋊ C5×#1600 |
640 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 98 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 — 3 generators on 24 points:
(1,2,3,4,5)(6,7)(9,11,12,15)(10,13,14,16)(19,23)(21,24);(7,8)(9,10)(11,13)(12,14)(15,16)(17,18)(19,24)(20,22)(21,23);(13,16)(18,21)(19,23)(22,24)210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 13598);