Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×C5×#2529 |
| 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 | |
796 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)(9,10)(11,13)(12,15)(14,16)(17,18,20,22)(19,21,23,24)(27,31)(30,32);(10,11)(14,15)(17,18,20,22)(19,21,23,24)(25,26,29,28)(27,30,31,32);(9,11,13,10)(12,15,16,14)(17,18)(19,21)(20,22)(23,24)(25,27)(26,30)(28,32)(29,31);(9,12,13,16)(10,14,11,15)(17,19,20,23)(18,21,22,24)(25,28,29,26)(27,32,31,30)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1261);