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×#3564 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C3×C5 |
| prime radical | C3×C5×#538 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
1872 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 5 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,14,18)(11,19,20,16)(12,23,26,17)(13,15,25,29)(21,31,33,32)(22,30,34,27)(24,37,38,28)(35,40,36,39);(10,15)(11,20)(12,24)(16,30)(18,29)(19,27)(21,35)(22,34)(26,38)(31,32)(33,36)(39,40);(9,11,13,22)(10,16,15,27)(12,21,24,36)(14,20,25,34)(17,31,28,39)(18,19,29,30)(23,32,37,40)(26,33,38,35);(9,12,25,38)(10,17,29,37)(11,21,34,35)(13,24,14,26)(15,28,18,23)(16,31,30,40)(19,32,27,39)(20,33,22,36);(10,15)(16,27)(17,28)(18,29)(19,30)(23,37)(31,39)(32,40)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2296);