Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C3×#66132 |
| Hall | C3×C5 ⋊ #518 |
| Sylow | C5 ⋊ C3×#518 |
676 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 382 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 — 4 generators on 20 points:
(1,2,3)(4,5,7,8,6)(14,18)(17,20);(15,19)(17,20);(13,15)(14,17)(16,19)(18,20);(5,6)(7,8)(9,10,11,12)(13,14)(15,17)(16,18)(19,20)222 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10600813, #14298645, C3×#10600860, … |
| maximal normal subgroup of | C3×#10600813, #14298645, C3×#10600860, … |
| maximal quotient of | C3×#10613814, C3×#10613875, C3×#10614048, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10004);