Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#65402 |
| Fitting | C22×C3×C5×C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #416 |
| Sylow | C5 ⋊ C3×#416 |
316 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 126 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)(13,16,15,22,18,25,17,24)(14,20,26,28,21,27,19,23);(13,15,18,17)(14,19,21,26)(16,22,25,24)(20,23,27,28);(5,6)(7,8)(13,14)(15,19)(16,23)(17,26)(18,21)(20,24)(22,27)(25,28)276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10599719, C3×#10600582, #14295958, … |
| maximal normal subgroup of | C3×#10599719, C3×#10600582, #14295958, … |
| maximal quotient of | C3×#10600527, C3×#10601553, C3×#10601556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4205);