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×#2533 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C3×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C3×C5 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ G | |
728 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 4 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10,12,14)(11,13,15,16)(17,18,21,24)(19,23,20,22)(27,31)(30,32);(9,10,12,14)(11,13,15,16)(17,19,21,20)(18,22,24,23)(25,26,29,28)(27,30,31,32);(9,10)(11,13)(12,14)(15,16)(17,20,21,19)(18,23,24,22)(25,27)(26,30)(28,32)(29,31);(9,11,12,15)(10,13,14,16)(17,18)(19,22)(20,23)(21,24)(25,28,29,26)(27,32,31,30)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1265);