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×#125 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3×C4×C5 | C23 |
| commutator | C22 | C23×C3×C4×C5 |
| Frattini, cosocle | C23 | C24×C3×C5 |
| socle, prime radical | C23×C3×C5 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C4×C5 ◁ G | |
968 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 4 generators on 28 points:
(1,2,3)(4,5,6,7)(24,25,26,27,28);(10,14)(12,15)(16,17,19,21)(18,20,22,23);(8,9,11,13)(10,12,14,15)(16,17)(18,20)(19,21)(22,23);(8,10)(9,12)(11,14)(13,15)(16,18,19,22)(17,20,21,23)840 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1037);