Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#65097 |
| Fitting | C3×C5×#103 ⋊ C2 |
| Hall | C3×C5 ⋊ #451 |
| Sylow | C5 ⋊ C3×#451 |
296 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,7,8,6)(9,10,11,12)(14,19)(15,21)(17,24)(18,25)(22,23)(26,28);(13,15,16,22)(14,18,19,26)(17,21,24,23)(20,28,27,25);(5,6)(7,8)(10,12)(13,14)(15,18)(16,19)(17,20)(21,28)(22,26)(23,25)(24,27)141 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#451, C2×C3×#65097, #14423365, … |
| maximal normal subgroup of | C3×D5×#451, C2×C3×#65097, #14423365, … |
| maximal quotient of | C3×#10599111, C3×#10599120, C3×#10599115, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3900);