Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#67773 |
| Hall | C3×C5 ⋊ #1405 |
| Sylow | C3 ⋊ C5×#1405 |
212 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 50 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)(6,8)(7,11)(9,12)(10,14)(13,20)(15,16)(17,19)(18,21)(22,23,24);(6,7,9,13,11,8,15,17)(10,14,20,12,21,18,19,16)(23,24)165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 5064);