Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#1867 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #120 |
| commutator | C23 | C22×C3×C4×C5 |
| Frattini, cosocle | C24 | C23×C3×C5 |
| prime radical | C22×C3×C5×D4 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C24×C3×C5 ◁ G | |
748 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(4,5,6,7,8)(9,10,12,11)(17,20);(9,11,12,10)(13,14)(15,17)(16,18)(19,20);(13,15)(14,17)(16,19)(18,20)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 599);