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×#2647 |
| 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 | |
720 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)(10,11)(14,15)(17,18)(19,22)(20,23)(21,24)(25,26,29,27)(28,31,32,30);(9,10,13,11)(12,14,16,15)(17,19)(18,20)(21,23)(22,24)(25,27,29,26)(28,30,32,31);(9,11,13,10)(12,14,16,15)(17,19)(18,22)(20,24)(21,23)(25,28,29,32)(26,30,27,31);(9,12,13,16)(10,14,11,15)(17,20,21,22)(18,23,24,19)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1379);