Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of AΣL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#2120 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | #99 |
| commutator | C23 | C22×C3×C4×C5 |
| Frattini, cosocle | C2×D4 | C23×C3×C5 |
| socle | C2×C3×C5 | C2×#99 |
| prime radical | C3×C5×#525 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C2×C3×C4×C5 ◁ C2×C3×C5×#41 ◁ G | |
528 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,15)(12,19,20,14)(13,16)(17,23,24,21)(18,22);(10,14)(15,21)(16,19)(22,23);(9,11,13,18)(10,15,16,22)(12,17,20,24)(14,21,19,23)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 852);