Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#69494 |
| Fitting | C3×C4×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #1806 |
| Sylow | C3 ⋊ C5×#1806 |
624 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(6,7)(13,15)(14,17)(16,18)(19,20);(9,10,11,12);(7,8)(10,12)(13,14,16,19,17,15,20,18)390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 23514);