Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#1664 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C3×C5 |
| prime radical | C2×C3×C5×D4 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G | |
368 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,14,18)(11,19,21,24)(12,17,13,16)(15,22,23,20)(25,26,30,28)(27,33,36,40)(29,37,39,32)(31,38,34,35);(9,11)(10,15)(12,22)(13,20)(14,21)(16,24)(17,19)(18,23)(25,27,30,36)(26,31,28,34)(29,38,39,35)(32,40,37,33);(9,11)(10,15)(12,20)(13,22)(14,21)(16,19)(17,24)(18,23)(25,28,30,26)(27,34,36,31)(29,32,39,37)(33,38,40,35)300 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 396);