Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#66165 |
| Fitting | C2×C3×C5×#41 ⋊ C2 |
| Hall | C3×C5 ⋊ #548 |
| Sylow | C5 ⋊ C3×#548 |
580 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 226 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 — 4 generators on 20 points:
(1,2,3)(4,5,7,8,6)(10,12)(13,16,17,15)(14,18,19,20);(13,15,17,16)(14,18,19,20);(13,14,17,19)(15,20,16,18);(5,6)(7,8)(9,10)(11,12)195 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10615684, C3×#10611852, #14453486, … |
| maximal normal subgroup of | C3×#10615684, C3×#10611852, #14453486, … |
| maximal quotient of | C3×Q8×#685, C3×#10615820, C3×#10614192, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10037);