Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#5121 |
| Hall | C3×C5 ⋊ #428 |
| Sylow | C3 ⋊ C5×#428 |
236 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 142 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)(13,14,15,17,16,18,19,20);(14,18)(17,20);(7,8)(9,10,11,12)(14,17)(15,19)(18,20)210 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#68758, C5×#70068, #14299598, … |
| maximal normal subgroup of | C5×#68758, C5×#70068, #14299598, … |
| maximal quotient of | C5×#69850, C5×#69851, C5×#70752, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4815);