Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23×C4 |
| direct product | C5×#5221 |
| Hall | C3×C5 ⋊ #390 |
| Sylow | C3 ⋊ C5×#390 |
516 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 182 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) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(6,7,8)(14,16)(18,20);(17,18,19,20);(7,8)(9,10,11,12)(13,14)(15,16)240 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#67695, #14279125, C5×#72140, … |
| maximal normal subgroup of | C5×#67695, #14279125, C5×#72140, … |
| maximal quotient of | C5×#71563, C5×#71545, C5×#72131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4915);