Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#65920 |
| Fitting | C3×C5×#120 ⋊ C2 |
| Hall | C3×C5 ⋊ #525 |
| Sylow | C5 ⋊ C3×#525 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3 | C23×D5 |
| commutator, cosocle | C22×C5 | C24×C3 |
| Frattini | C22 | C23×C3×D5 |
| Fitting | C3×C5×#120 | C2 |
| socle | C22×C3×C5 | C24 |
| hypercenter | C3×#120 | D5 |
| hypocenter | C5 | C3×#525 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C3 ◁ C3×#120 | |
660 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 4 generators on 20 points:
(1,2,3)(4,5,7,8,6)(10,12)(15,19)(17,20);(9,10)(11,12);(13,15)(14,17)(16,19)(18,20);(5,6)(7,8)(13,14,16,18)(15,17,19,20)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10604463, #14301717, C3×#10599929, … |
| maximal normal subgroup of | C3×#10604463, #14301717, C3×#10599929, … |
| maximal quotient of | C3×#10605548, C3×#10606108, C3×#10606388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9792);