Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C24×C4 |
| direct product | C5×#5607 |
| Fitting | C3×C5×#121 ⋊ C2 |
| Hall | C3×C5 ⋊ #535 |
| Sylow | C3 ⋊ C5×#535 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C5 | C23×D3 |
| commutator, cosocle | C22×C3 | C24×C5 |
| Frattini | C22 | C23×C5×D3 |
| Fitting | C3×C5×#121 | C2 |
| socle | C22×C3×C5 | C24 |
| hypercenter | C5×#121 | D3 |
| hypocenter | C3 | C5×#535 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22×C5 ◁ C5×#121 | |
668 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)(6,7,8)(9,10)(11,12)(14,18)(17,20);(10,12)(15,19)(17,20);(10,12)(13,15)(14,17)(16,19)(18,20);(7,8)(13,14)(15,17)(16,18)(19,20)180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#80004, C5×#80085, #14424233, … |
| maximal normal subgroup of | C5×#80004, C5×#80085, #14424233, … |
| maximal quotient of | C5×#76428, C5×#74003, C5×#75968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10187);