Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×C5×#2158 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | D8 |
| commutator | C8 | C22×C3×C4×C5 |
| Frattini, cosocle | C2×C8 | C23×C3×C5 |
| socle | C22×C3×C5 | C2×D8 |
| prime radical | C23×C3×C5 | D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ C22×C3×C4×C5 ◁ C22×C3×C5×C8 ◁ G | |
304 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 44 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12)(13,14)(15,24)(16,21)(17,31)(18,33)(19,23)(20,27)(22,25)(26,37)(28,43)(29,39)(30,36)(32,44)(34,41)(35,42)(38,40);(13,15,25,40,18,28,32,42,19,29,30,41,16,26,17,27)(14,20,31,37,21,34,36,39,23,35,44,43,33,38,22,24);(13,16,19,18)(14,21,23,33)(15,26,29,28)(17,30,32,25)(20,34,35,38)(22,31,36,44)(24,37,39,43)(27,41,42,40)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 890);