Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#3069 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | C2×#121 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| prime radical | C3×C5×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
892 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)(9,10,15,20)(11,21,23,32)(12,26,28,34)(13,19,14,18)(16,25,31,24)(17,29,33,27)(22,36,37,30)(35,39,40,38);(9,11,13,24,15,23,14,25)(10,16,18,21,20,31,19,32)(12,22,27,38,28,37,29,39)(17,30,26,35,33,36,34,40);(9,12)(10,17)(11,22)(13,27)(14,29)(15,28)(16,30)(18,26)(19,34)(20,33)(21,35)(23,37)(24,38)(25,39)(31,36)(32,40);(11,23)(16,31)(21,32)(22,37)(24,25)(30,36)(35,40)(38,39)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1801);