Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1714 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C4 |
| direct product | C3×C5×#1718 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C3×C5 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C3×C5 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G | |
328 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)(9,10,13,16)(11,17,18,24)(12,20,21,15)(14,22,23,19)(25,26)(27,33)(28,30)(29,37)(31,35)(32,36)(34,39)(38,40);(9,11,12,19,13,18,21,22)(10,14,15,17,16,23,20,24)(26,30)(31,38)(32,37)(33,39);(11,18)(14,23)(17,24)(19,22)(25,27,29,35,28,34,36,40)(26,31,32,33,30,38,37,39)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 450);