Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3×C5 · Schur multiplier (H2) = C28 |
| direct product | C3×C5×#3552 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C3×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
2008 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)(9,10)(11,12)(13,14)(15,16)(18,23)(19,20)(21,29)(31,32);(10,14)(11,15)(17,18,22,23)(19,25,20,24)(21,26,29,30)(27,32,28,31);(17,19,22,20)(18,24,23,25)(21,27,29,28)(26,31,30,32);(9,11,13,15)(10,12,14,16)(17,20,22,19)(18,25,23,24)(21,28,29,27)(26,32,30,31);(9,12)(10,15)(11,14)(13,16)(17,21)(18,26)(19,27)(20,28)(22,29)(23,30)(24,31)(25,32)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2284);