Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#67699 |
| Hall | C3×C5 ⋊ #1394 |
| Sylow | C3 ⋊ C5×#1394 |
344 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3,4,5)(7,8)(9,10,11,12)(14,18,21,19)(20,27,28,26);(6,7,8)(13,14,16,20,17,21,25,28)(15,19,22,27,23,18,24,26)240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 4828);