Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3×C5 · Schur multiplier (H2) = C28 |
| direct product | C3×C5×#3565 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C3×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×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)(9,10,13,14)(11,17,18,15)(12,20,21,16)(19,22,24,23)(25,26)(27,32)(28,33)(29,37)(30,31)(34,38)(35,36)(39,40);(10,14)(11,18)(16,20)(19,24)(26,31)(28,32)(34,37)(36,39);(9,11,13,18)(10,15,14,17)(12,19,21,24)(16,22,20,23)(25,27,30,33)(26,32,31,28)(29,35,38,40)(34,39,37,36);(9,10)(11,15)(12,16)(13,14)(17,18)(19,22)(20,21)(23,24)(25,28,30,32)(26,33,31,27)(29,36,38,39)(34,40,37,35);(9,12,13,21)(10,16,14,20)(11,19,18,24)(15,22,17,23)(25,29,30,38)(26,34,31,37)(27,35,33,40)(28,36,32,39)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2297);