Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#67542 |
| Fitting | C3×C5×#354 ⋊ C2 |
| Hall | C3×C5 ⋊ #1404 |
| Sylow | C3 ⋊ C5×#1404 |
224 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 224 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)(6,7)(8,15)(9,18)(10,14)(11,17)(12,16)(13,20)(19,21)(23,24);(6,7,8,12)(9,18,19,15)(10,14,17,21)(11,20,13,16)(22,23,24)150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 5038);