Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#2646 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C3×C5 |
| prime radical | C24×C3×C5 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ G | |
872 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)(9,10,13,14)(11,12,15,16)(18,19)(22,23)(25,26)(27,30)(28,31)(29,32);(10,14)(11,15)(17,18,21,19)(20,22,24,23)(25,27)(26,29)(28,32)(30,31);(9,11)(10,12)(13,15)(14,16)(17,19,21,18)(20,22,24,23)(25,27)(26,30)(28,32)(29,31);(9,12)(10,15)(11,14)(13,16)(17,20)(18,22)(19,23)(21,24)(25,26)(27,29)(28,31)(30,32)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1378);