Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#3293 |
| 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 | |
888 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)(9,10,16,21)(11,22,25,27)(12,24,17,31)(13,18,30,36)(14,20,15,19)(23,38,40,34)(26,39,33,28)(29,37,32,35);(9,11,16,25)(10,17,21,12)(13,28,30,39)(14,31,15,24)(18,34,36,38)(19,27,20,22)(23,32,40,29)(26,35,33,37);(9,12,16,17)(10,11,21,25)(13,26,30,33)(14,27,15,22)(18,23,36,40)(19,24,20,31)(28,37,39,35)(29,38,32,34);(9,13)(10,18)(11,23)(12,26)(14,32)(15,29)(16,30)(17,33)(19,37)(20,35)(21,36)(22,38)(24,39)(25,40)(27,34)(28,31)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2025);