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×#3555 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C3×C5 |
| prime radical | C3×C5×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
1820 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)(9,10,14,17)(11,12,19,15)(13,21,22,16)(18,23,24,20)(25,26,29,32)(27,30,35,33)(28,36,37,31)(34,39,40,38);(9,11,14,19)(10,15,17,12)(13,18,22,24)(16,23,21,20)(25,26)(27,33)(28,31)(29,32)(30,35)(34,39)(36,37)(38,40);(9,12,14,15)(10,11,17,19)(13,20,22,23)(16,18,21,24);(9,11)(10,15)(12,17)(13,18)(14,19)(16,23)(20,21)(22,24)(25,27)(26,30)(28,34)(29,35)(31,38)(32,33)(36,39)(37,40);(9,13,14,22)(10,16,17,21)(11,18,19,24)(12,20,15,23)(25,28,29,37)(26,31,32,36)(27,34,35,40)(30,38,33,39)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2287);