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) = C24 |
| direct product | C3×C5×#2644 |
| 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 | |
840 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)(10,13)(14,15)(17,18)(19,22)(20,23)(21,24)(25,26,29,31)(27,32,28,30);(9,10,12,13)(11,14,16,15)(17,19)(18,20)(21,23)(22,24)(25,27,29,28)(26,30,31,32);(9,10)(11,15)(12,13)(14,16)(17,19)(18,22)(20,24)(21,23)(25,26)(27,30)(28,32)(29,31);(9,11,12,16)(10,14,13,15)(17,20,21,22)(18,23,24,19)(25,28,29,27)(26,30,31,32)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1376);