Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#2681 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C3×C5 |
| prime radical | C2×C3×C5×#121 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ G | |
1236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12)(17,18)(19,24)(20,21)(22,23);(14,16)(17,19,22,20)(18,21,23,24);(9,10)(11,12)(13,14)(15,16)(17,20,22,19)(18,21,23,24);(9,10)(11,12)(17,21)(18,19)(20,23)(22,24)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1413);