Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1595 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#1615 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3×C5 |
| prime radical | C3×C5×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
416 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,16,26)(11,20,31,40)(12,14,19,15)(13,25,32,36)(17,33,39,22)(18,29,28,30)(21,37,34,27)(23,35,24,38);(9,11)(10,17)(12,21)(13,27)(14,24)(15,23)(16,31)(18,35)(19,34)(20,25)(22,30)(26,39)(28,38)(29,33)(32,37)(36,40);(9,12,15,10)(11,21,23,17)(13,28,30,36)(14,26,16,19)(18,29,25,32)(20,37,35,33)(22,40,27,38)(24,39,31,34)345 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 347);