Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3×C5 · Schur multiplier (H2) = C28 |
| direct product | C3×C5×#3531 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C3×C5 |
| socle | C22×C3×C5 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ G | |
1860 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)(11,17)(12,16)(13,15)(14,18)(19,23)(20,22)(21,24)(25,26)(27,30)(28,35)(29,32)(31,37)(33,40)(34,39)(36,38);(9,11)(10,14)(12,19)(13,18)(15,17)(16,21)(20,24)(22,23)(25,27,29,34)(26,30,32,39)(28,36,37,33)(31,40,35,38);(11,18)(14,17)(19,24)(21,23)(25,28,29,37)(26,31,32,35)(27,33,34,36)(30,38,39,40);(10,15)(11,18)(16,22)(19,24)(26,32)(30,39)(31,35)(38,40);(9,12,13,20)(10,16,15,22)(11,19,18,24)(14,21,17,23)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2263);