Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#2166 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | #117 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C2×C8 | C23×C3×C5 |
| socle | C2×C3×C5 | #432 |
| prime radical | C23×C3×C5 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C3×C5×#97 ◁ G | |
244 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,12,18,13,19,26,35,14,17,25,33,27,16,30,32)(11,20,22,34,23,31,37,40,21,15,24,29,36,28,38,39);(9,11)(10,15)(12,24)(13,23)(14,21)(16,31)(17,20)(18,34)(19,28)(22,25)(26,38)(27,36)(29,33)(30,37)(32,39)(35,40);(10,16,17,19)(11,21)(12,25)(15,28,20,31)(18,35,33,32)(23,36)(26,30)(29,40,34,39)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 898);