Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#68970 |
| Fitting | C3×C5×#342 ⋊ C2 |
| Hall | C3×C5 ⋊ #1898 |
| Sylow | C3 ⋊ C5×#1898 |
1196 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(6,7)(10,12);(13,15)(14,17,18,20)(16,19);(7,8)(9,10)(11,12)(13,14)(15,17,19,20)(16,18)270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 27736);