Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#3232 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| prime radical | C3×C5×#121 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C2×C3×C42×C5 ◁ G | |
668 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,17)(12,15)(13,16)(14,19)(18,23)(20,22)(21,24)(25,26)(27,30)(28,31)(29,33)(32,36)(34,37)(35,39)(38,40);(9,11,13,19)(10,14,16,17)(12,20,21,18)(15,23,24,22)(25,27,29,35)(26,30,33,39)(28,34,36,40)(31,37,32,38);(9,12,13,21)(10,15,16,24)(11,18,19,20)(14,22,17,23)(26,31)(28,36)(30,37)(32,33)(34,40)(38,39);(10,16)(14,17)(15,24)(22,23)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1964);