Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3×C5 · Schur multiplier (H2) = C28 |
| direct product | C3×C5×#3523 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C3×C5 |
| prime radical | C3×C5×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
1984 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 5 generators on 32 points:
(1,2,3)(4,5,6,7,8)(10,13)(14,16)(17,18,22,20)(19,25,27,23)(21,28,29,24)(26,30,32,31);(17,19,22,27)(18,23,20,25)(21,26,29,32)(24,30,28,31);(9,10)(11,14)(12,13)(15,16);(17,20,22,18)(19,23,27,25)(21,28,29,24)(26,30,32,31);(9,11,12,15)(10,14,13,16)(17,21,22,29)(18,24,20,28)(19,26,27,32)(23,30,25,31)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2255);