Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#564 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C3×C5 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C3×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
344 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 40 points:
(1,2,3)(4,5,6,7,8)(11,17)(12,20)(14,18)(15,22)(25,26,29,32)(27,30,35,33)(28,36,37,31)(34,39,40,38);(9,10,13,16)(11,18,17,14)(12,15,20,22)(19,24,23,21)(25,26)(27,33)(28,36)(29,32)(30,35)(31,37)(34,38)(39,40);(9,11,13,17)(10,14,16,18)(12,19,20,23)(15,21,22,24)(25,27)(26,30)(28,34)(29,35)(31,38)(32,33)(36,39)(37,40);(9,12)(10,15)(11,19)(13,20)(14,21)(16,22)(17,23)(18,24)(25,28,29,37)(26,31,32,36)(27,34,35,40)(30,38,33,39)285 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10848);