Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4532 |
| Hall | C3×C5 ⋊ #339 |
| Sylow | C3 ⋊ C5×#339 |
220 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3,4,5)(6,7,8)(9,10,11,12)(13,15,17,14)(16,20,18,19);(7,8)(13,14,16,19,17,15,18,20)240 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#339, C2×C5×#4532, D5×#4532, … |
| maximal normal subgroup of | C5×D3×#339, C2×C5×#4532, D5×#4532, … |
| maximal quotient of | C5×#67736, C5×#67739, C5×#67619, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 426);