Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#65444 |
| Hall | C3×C5 ⋊ #495 |
| Sylow | C5 ⋊ C3×#495 |
260 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 86 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)(10,12)(14,19)(15,22)(16,25)(18,26)(21,28)(23,24);(10,12)(13,15)(14,18)(16,22)(17,24)(19,21)(20,28)(23,25)(26,27);(5,6)(7,8)(9,10,11,12)(13,14)(15,21)(16,20)(17,19)(18,24)(22,26)(23,28)(25,27)150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598800, #14278434, C3×#10602256, … |
| maximal normal subgroup of | C3×#10598800, #14278434, C3×#10602256, … |
| maximal quotient of | C3×#10602067, C3×#10602153, C3×#10601974, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4247);