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×#3532 |
| 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 | |
2672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 5 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,17)(12,16)(13,15)(14,19)(18,21)(20,23)(22,24);(9,11)(10,14)(12,19)(13,18)(15,22)(16,17)(20,24)(21,23);(10,15)(11,18)(16,23)(19,24);(10,15)(11,19)(14,21)(16,23)(17,22)(18,24);(10,16)(14,17)(15,23)(21,22)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2264);