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) = C22×C42 |
| direct product | C3×C5×H(3,𝔽4) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C3×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10,13,16)(11,18,19,15)(12,20,22,24)(14,17,23,21);(9,11,13,19)(10,15,16,18)(12,21,22,17)(14,20,23,24);(9,12)(10,11)(13,22)(14,15)(16,19)(17,20)(18,23)(21,24);(9,11)(10,12)(13,19)(14,20)(15,17)(16,22)(18,21)(23,24)285 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10845);