Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C26 |
| direct product | C3×C5×#3028 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | C2×#120 |
| commutator, Frattini, cosocle | C23 | C24×C3×C5 |
| prime radical | C3×C5×#585 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
1432 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,14,18)(11,15,21,28)(12,16,23,30)(13,24,25,17)(19,31,33,26)(20,34,35,27)(22,36,37,29)(32,38,40,39);(9,11)(10,15)(12,19)(13,20)(14,21)(16,26)(17,27)(18,28)(22,32)(23,33)(24,34)(25,35)(29,38)(30,31)(36,39)(37,40);(9,12)(10,16)(11,19)(13,22)(14,23)(15,26)(17,29)(18,30)(20,32)(21,33)(24,36)(25,37)(27,38)(28,31)(34,39)(35,40);(9,13,14,25)(10,17,18,24)(11,20,21,35)(12,22,23,37)(15,27,28,34)(16,29,30,36)(19,32,33,40)(26,38,31,39)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1760);