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×#3568 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C3×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
1916 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)(9,10,14,16)(11,20,24,22)(12,15,19,25)(13,27,28,18)(17,31,30,21)(23,36,37,34)(26,38,33,29)(32,35,39,40);(10,16)(11,21)(12,19)(17,22)(18,27)(20,30)(23,35)(24,31)(26,33)(32,36)(34,39)(37,40);(9,11,14,24)(10,17,16,30)(12,22,19,20)(13,23,28,37)(15,21,25,31)(18,32,27,39)(26,36,33,34)(29,35,38,40);(9,12,25,10)(11,22,31,17)(13,26,38,18)(14,19,15,16)(20,21,30,24)(23,36,40,32)(27,28,33,29)(34,35,39,37);(9,13,25,38)(10,18,12,26)(11,23,31,40)(14,28,15,29)(16,27,19,33)(17,32,22,36)(20,34,30,39)(21,35,24,37)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2300);