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×#3567 |
| 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 | |
1900 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)(10,14)(11,17)(16,21)(18,23)(25,26)(27,30)(28,33)(29,34)(31,35)(32,37)(36,38)(39,40);(10,14)(15,20)(16,21)(22,24)(26,27)(28,35)(32,34)(36,40);(9,10)(11,15)(12,16)(13,14)(17,20)(18,22)(19,21)(23,24)(25,27,30,26)(28,33,35,31)(29,34,37,32)(36,39,40,38);(9,11,13,17)(10,15,14,20)(12,18,19,23)(16,22,21,24)(25,28)(26,31)(27,33)(29,36)(30,35)(32,38)(34,39)(37,40);(9,12,13,19)(10,16,14,21)(11,18,17,23)(15,22,20,24)(25,29)(26,32)(27,34)(28,36)(30,37)(31,38)(33,39)(35,40)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2299);