Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#71102 |
| Hall | C3×C5 ⋊ #1679 |
| Sylow | C3 ⋊ C5×#1679 |
332 conjugacy classes of subgroups.
| 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)(10,14)(12,16)(13,15);(7,8)(10,13)(14,15)(17,19,20,18,21,22,24,23);(9,10)(11,13)(12,14)(15,16)(17,18,21,23)(19,24,22,20)240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 17668);