Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#2003 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3×C5 |
| prime radical | C2×C3×C5×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
764 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,12)(13,14)(15,19)(16,18)(17,21)(20,24)(22,27)(23,28)(25,26);(14,18)(16,24)(19,27)(20,21)(22,25)(26,28);(10,12)(13,15,17,23)(14,19,21,28)(16,25,24,22)(18,26,20,27)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 735);