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×#3563 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C3×C5 |
| prime radical | C3×C5×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
1824 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)(9,10)(11,18)(12,15)(13,21)(14,17)(16,22)(19,23)(20,24)(25,26,31,34)(27,29,32,28)(30,38,39,33)(35,36,40,37);(9,11,14,12)(10,15,17,18)(13,19,22,20)(16,23,21,24)(25,27,31,32)(26,28,34,29)(30,35,39,40)(33,36,38,37);(9,12,14,11)(10,15,17,18)(13,20,22,19)(16,23,21,24)(25,28,31,29)(26,32,34,27)(30,36,39,37)(33,40,38,35);(9,10)(11,18)(12,15)(13,16)(14,17)(19,24)(20,23)(21,22)(25,29,31,28)(26,27,34,32)(30,37,39,36)(33,35,38,40);(9,13)(10,16)(11,19)(12,20)(14,22)(15,23)(17,21)(18,24)(25,30)(26,33)(27,35)(28,36)(29,37)(31,39)(32,40)(34,38)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2295);