Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1705 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22×C8 |
| direct product | C3×C5×#1712 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C3×C5 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G | |
560 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,6,7,8)(10,13)(11,14)(15,16)(18,21)(19,22)(23,24);(9,10,14,16,12,15,11,13);(17,18,22,24,20,23,19,21)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 444);