Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#68941 |
| Fitting | C3×C5×#341 ⋊ C2 |
| Hall | C3×C5 ⋊ #1855 |
| Sylow | C3 ⋊ C5×#1855 |
556 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3,4,5)(6,7)(10,12);(13,15,17,23,18,24,16,26)(14,19,20,27,21,28,25,22);(7,8)(9,10)(11,12)(13,14,17,20,18,21,16,25)(15,22,23,19,24,27,26,28)330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 25214);