Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#532 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C3×C5 |
| socle | C22×C3×C5 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ G | |
620 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 20 points:
(1,2,3)(4,5,6,7,8)(10,12)(13,14)(15,18)(16,17)(19,20);(14,17)(18,20);(9,10,11,12);(13,15,16,19)(14,18,17,20)420 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10816);