Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C4×C5×#126 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3×C4×C5 | C23 |
| commutator | C22 | C23×C3×C4×C5 |
| Frattini, cosocle | C23 | C24×C3×C5 |
| socle | C23×C3×C5 | C24 |
| prime radical | C24×C3×C5 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C4×C5 ◁ G | |
1032 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 28 points:
(1,2,3)(4,5,6,7)(24,25,26,27,28);(9,13)(10,17)(15,22)(16,20)(18,21)(19,23);(8,9,14,20)(10,15,21,22)(11,13,12,16)(17,23,18,19);(8,10,11,18)(9,15,13,19)(12,17,14,21)(16,23,20,22)840 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1036);