Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#65932 |
| Fitting | C3×C5×#121 ⋊ C2 |
| Hall | C3×C5 ⋊ #548 |
| Sylow | C5 ⋊ C3×#548 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3 | C23×D5 |
| commutator, cosocle | C22×C5 | C24×C3 |
| Frattini | C22 | C23×C3×D5 |
| Fitting | C3×C5×#121 | C2 |
| socle | C22×C3×C5 | C24 |
| hypercenter | C3×#121 | D5 |
| hypocenter | C5 | C3×#548 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C3 ◁ C3×#121 | |
580 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)(4,5,7,8,6)(10,12)(15,20)(17,19);(9,10)(11,12);(13,15,16,20)(14,17,18,19);(5,6)(7,8)(13,14,16,18)(15,19,20,17)159 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10612458, C3×#10611756, #14453528, … |
| maximal normal subgroup of | C3×#10612458, C3×#10611756, #14453528, … |
| maximal quotient of | C3×#10605607, C3×#10608032, C3×#10607713, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9804);