Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#3067 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | #121 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| socle | C2×C3×C5 | C2×#121 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C22×C3×C4×C5 ◁ G | |
904 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)(11,21)(12,26)(13,18)(14,19)(15,20)(16,23)(17,27)(22,36)(24,32)(25,31)(28,33)(29,34)(30,38)(35,37)(39,40);(9,11,13,23,15,25,14,24)(10,16,19,21,20,32,18,31)(12,22,27,37,28,38,29,39)(17,30,26,35,34,36,33,40);(9,12)(10,17)(11,22)(13,27)(14,29)(15,28)(16,30)(18,33)(19,26)(20,34)(21,35)(23,37)(24,39)(25,38)(31,40)(32,36);(9,13,15,14)(10,18,20,19)(11,23,25,24)(12,27,28,29)(16,31,32,21)(17,33,34,26)(22,37,38,39)(30,40,36,35)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1799);