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) = C23 |
| direct product | C3×C5×#1813 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | #117 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C3×C5 |
| socle | C2×C3×C5 | #380 |
| prime radical | C2×C3×C5×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C2×C3×C5×M16 ◁ G | |
504 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)(9,10,14,18,15,19,13,28)(11,20,23,31,24,35,22,16)(12,25,26,32,27,17,29,33)(21,36,37,40,38,34,39,30);(9,11,13,22,15,24,14,23)(10,16,18,20,19,31,28,35)(12,21,26,37,27,38,29,39)(17,30,32,34,25,40,33,36);(9,12)(10,17)(11,21)(13,26)(14,29)(15,27)(16,30)(18,32)(19,25)(20,34)(22,37)(23,39)(24,38)(28,33)(31,40)(35,36)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 545);