Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3×C5 · Schur multiplier (H2) = C27×C4 |
| direct product | C3×C5×#3549 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C3×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
2516 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 5 generators on 24 points:
(1,2,3)(4,5,6,7,8)(10,12)(14,15)(18,21)(19,20);(9,10,13,12)(11,15,16,14)(17,18,22,21)(19,24,20,23);(17,19,22,20)(18,23,21,24);(9,11,13,16)(10,14,12,15)(17,20,22,19)(18,24,21,23);(9,12,13,10)(11,15,16,14)(17,21,22,18)(19,24,20,23)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2281);