Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#2510 |
| 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 | |
964 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)(11,13)(12,15)(14,16)(17,18,21,23)(19,20,24,22)(25,26,28,30)(27,31,32,29);(10,11)(14,15)(17,19,21,24)(18,22,23,20)(25,26)(27,29)(28,30)(31,32);(9,11,13,10)(12,15,16,14)(17,19)(18,20)(21,24)(22,23)(25,27,28,32)(26,29,30,31);(9,12)(10,14)(11,15)(13,16)(17,20)(18,19)(21,22)(23,24)(25,26)(27,29)(28,30)(31,32)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1242);