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) = C28 |
| direct product | C3×C5×#3536 |
| 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 | |
2268 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)(9,10)(11,15)(12,13)(14,16)(18,21)(19,23);(10,13)(14,15)(18,21)(22,24);(17,18)(19,22)(20,21)(23,24);(9,10)(11,14)(12,13)(15,16)(17,19)(18,22)(20,23)(21,24);(9,11,12,16)(10,14,13,15)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2268);