Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3288 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#3289 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ G | |
896 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,15,21)(11,22,26,37)(12,18,28,36)(13,20,14,19)(16,29,33,25)(17,30,34,27)(23,31,40,32)(24,38,39,35);(9,11,15,26)(10,16,21,33)(12,23,28,40)(13,29,14,25)(17,31,34,32)(18,35,36,38)(19,37,20,22)(24,30,39,27);(9,12)(10,17)(11,23)(13,27)(14,30)(15,28)(16,31)(18,19)(20,36)(21,34)(22,38)(24,29)(25,39)(26,40)(32,33)(35,37);(9,12)(10,18)(11,24)(13,30)(14,27)(15,28)(16,32)(17,19)(20,34)(21,36)(22,38)(23,29)(25,40)(26,39)(31,33)(35,37)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2021);