Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#1840 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3×C4×C5 | C23 |
| commutator | C23 | C22×C3×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C3×C5 |
| socle, prime radical | C23×C3×C5 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C4×C5 ◁ G | |
392 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 3 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,16)(12,14)(13,15)(17,18)(19,21)(20,22)(23,24)(25,26,28,31,29,32,35,38)(27,30,34,37,33,36,39,40);(9,11,13,12)(10,14,15,16)(17,19,20,23)(18,21,22,24)(25,27)(26,30)(28,34)(29,33)(31,37)(32,36)(35,39)(38,40);(9,12,13,11)(10,14,15,16)(18,22)(21,24)(27,33)(30,36)(34,39)(37,40)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 572);