Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#2667 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C3×C5 |
| prime radical | C24×C3×C5 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ G | |
816 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 32 points:
(1,2,3)(4,5,6,7,8)(10,13)(14,16)(18,21)(22,23)(27,31)(30,32);(17,18,20,21)(19,22,24,23)(25,26,29,28)(27,32,31,30);(9,10)(11,14)(12,13)(15,16)(17,18)(19,23)(20,21)(22,24)(25,27,29,31)(26,30,28,32);(9,11,12,15)(10,14,13,16)(17,19,20,24)(18,22,21,23)(25,28,29,26)(27,32,31,30)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1399);