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) = C23 |
| direct product | C3×C5×#2743 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C3×C5 |
| prime radical | C22×C3×C5×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ G | |
896 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10,13,11)(12,15,16,14)(17,18)(19,20)(21,22)(23,24)(25,26)(27,30)(28,32)(29,31);(10,11)(12,16)(18,22)(20,24)(25,27,29,32)(26,30,31,28);(9,11,13,10)(12,15,16,14)(17,19,21,23)(18,20,22,24)(25,27)(26,28)(29,32)(30,31);(9,12)(10,14)(11,15)(13,16)(17,20)(18,23)(19,22)(21,24)(25,28)(26,27)(29,30)(31,32)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1475);