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×#3566 |
| 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 | |
1908 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 5 generators on 40 points:
(1,2,3)(4,5,6,7,8)(10,16)(11,21)(12,26)(13,29)(17,34)(18,24)(20,33)(22,32)(25,38)(27,35)(28,39)(30,40);(9,10)(11,22)(12,27)(13,19)(14,16)(15,20)(17,21)(18,28)(23,29)(24,26)(25,34)(30,36)(31,33)(32,38)(35,39)(37,40);(9,11,14,25)(10,17,16,32)(12,23,28,19)(13,24,29,35)(15,21,31,38)(18,30,27,40)(20,22,33,34)(26,37,39,36);(9,12)(10,18)(11,23)(13,22)(14,28)(15,26)(16,27)(17,30)(19,25)(20,35)(21,37)(24,33)(29,34)(31,39)(32,40)(36,38);(9,13,15,30)(10,19,20,36)(11,24,21,27)(12,22,26,17)(14,29,31,40)(16,23,33,37)(18,25,35,38)(28,34,39,32)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2298);