Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#338 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | C42 |
| commutator | C4 | C3×C42×C5 |
| Frattini, cosocle | C22×C4 | C22×C3×C5 |
| socle | C2×C3×C5 | #95 |
| prime radical | C23×C3×C5 | Q8 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ G | |
172 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10,12,16,14,17,13,22)(11,18,20,15,21,23,19,24);(9,11,13,20,14,21,12,19)(10,15,16,18,17,24,22,23)330 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 601);