Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C16 · Schur multiplier (H2) = C23 |
| direct product | C5×#67⋊C16 |
| unambiguous semidirect product | #67⋊(C5×C16) |
| Fitting | C3×C5×C22⋊C16 ⋊ C2 |
| Hall | C3×C5 ⋊ D4×C16 |
| Sylow | C3 ⋊ C5×D4×C16 |
348 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3,4,5)(7,8)(13,15,16,22,17,23,24,28,18,14,19,20,25,21,26,27);(6,7,8)(10,12);(9,10)(11,12)(13,14,16,20,17,21,24,27,18,15,19,22,25,23,26,28)600 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 40665);