Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#65479 |
| Fitting | C2×C3×C5×Q16 ⋊ C2 |
| Hall | C3×C5 ⋊ #497 |
| Sylow | C5 ⋊ C3×#497 |
248 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 248 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)(13,15,17,23)(14,19,20,28)(16,25,24,22)(18,26,27,21);(13,14,16,18,17,20,24,27)(15,21,22,28,23,26,25,19);(5,6)(7,8)(9,10)(11,12)(14,18)(16,24)(19,26)(20,27)(21,28)(22,25)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#497, C2×C3×#65479, #14439034, … |
| maximal normal subgroup of | C3×D5×#497, C2×C3×#65479, #14439034, … |
| maximal quotient of | C3×#10602156, C3×#10602009, C3×#10602092, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4282);