Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | C5×#5717 |
| Fitting | C3×C5×#127 ⋊ C2 |
| Hall | C3×C5 ⋊ D42 |
| Sylow | C3 ⋊ C5×D42 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C5 | C23×D3 |
| commutator, cosocle | C22×C3 | C24×C5 |
| Frattini | C22 | C23×C5×D3 |
| Fitting | C3×C5×#127 | C2 |
| socle | C22×C3×C5 | C24 |
| hypercenter | C5×#127 | D3 |
| hypocenter | C3 | C5×D42 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22×C5 ◁ C5×#127 | |
856 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 4 generators on 16 points:
(1,2,3,4,5)(6,7,8)(9,10,11,12)(13,15,16,14);(10,12)(13,14)(15,16);(10,12)(14,15);(7,8)(10,12)195 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#71281, C5×#68390, #14288823, … |
| maximal normal subgroup of | C5×#71281, C5×#68390, #14288823, … |
| maximal quotient of | C5×#76431, C5×#74360, C5×#76432, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10297);