Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#1554 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C42 | C23×C3×C5 |
| prime radical | C23×C3×C5 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C2×C3×C42×C5 ◁ G | |
396 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)(9,10,13,16,14,17,12,21)(11,18,19,23,20,15,22,24)(25,26)(27,33)(28,36)(29,31)(30,34)(32,38)(35,40)(37,39);(9,11,14,20)(10,15,17,18)(12,19,13,22)(16,23,21,24)(25,27,29,35)(26,30,31,39)(28,37,38,34)(32,40,36,33);(9,12,14,13)(10,16,17,21)(11,19,20,22)(15,23,18,24)(26,31)(30,39)(32,36)(33,40)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 286);