Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4×C5 · Schur multiplier (H2) = C24×C4 |
| direct product | C3×C5×#2342 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3×C5 | C24 |
| commutator | C22 | C23×C3×C4×C5 |
| Frattini, cosocle | C23 | C24×C3×C5 |
| prime radical | C25×C3×C5 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ G | |
1584 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,12)(13,14,15,16)(17,18)(19,23)(20,22)(21,24);(10,12)(17,18,20,22)(19,21,24,23);(17,19)(18,21)(20,24)(22,23);(9,10)(11,12)(17,18)(19,21)(20,22)(23,24)750 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1074);