Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3×C5 · Schur multiplier (H2) = C28 |
| direct product | C3×C5×#3556 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C3×C5 |
| prime radical | C23×C3×C5 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
1780 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 5 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,14,12)(11,17,19,15)(13,20,21,16)(18,22,24,23)(25,26,30,34)(27,32,28,31)(29,37,38,33)(35,39,36,40);(9,11,14,19)(10,15,12,17)(13,18,21,24)(16,22,20,23)(25,26)(27,32)(28,31)(29,33)(30,34)(35,40)(36,39)(37,38);(25,27,30,28)(26,31,34,32)(29,35,38,36)(33,39,37,40);(9,12,14,10)(11,15,19,17)(13,20,21,16)(18,22,24,23)(25,28,30,27)(26,32,34,31)(29,36,38,35)(33,40,37,39);(9,13,14,21)(10,16,12,20)(11,18,19,24)(15,22,17,23)(25,29,30,38)(26,33,34,37)(27,35,28,36)(31,39,32,40)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2288);