Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1665 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#1676 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C3×C5 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C3×C5 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G | |
288 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 3 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,13,16)(11,17,20,24)(12,21,18,15)(14,22,23,19)(25,26,29,32)(27,33,35,40)(28,36,38,31)(30,37,39,34);(9,11,18,22,13,20,12,19)(10,14,21,24,16,23,15,17);(25,27,29,35)(26,30,32,39)(28,37,38,34)(31,40,36,33)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 408);