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) = C27 |
| direct product | C3×C4×C5×#120 |
| 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 | C2×C3×C5×#120 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C4×C5 ◁ G | |
2448 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 20 points:
(1,2,3)(4,5,6,7)(16,17,18,19,20);(8,9)(10,12)(11,13)(14,15);(9,12)(13,15);(9,13)(12,15)840 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1031);