Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×#364 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C5×C8 | D4 |
| commutator | C4 | C2×C3×C5×C8 |
| Frattini, cosocle | C2×C8 | C22×C3×C5 |
| socle | C2×C3×C5 | C4⋊C8 |
| prime radical | C22×C3×C5 | M16 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C5×C8 ◁ C2×C3×C5×C8 ◁ G | |
92 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)(9,10,13,18,14,17,22,24,15,19,21,16,12,23,11,20);(9,11,12,21,15,22,14,13)(10,16,17,20,19,18,23,24)420 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 627);