Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65006 |
| Fitting | C3×C5×#97 ⋊ C2 |
| Hall | C3×C5 ⋊ #444 |
| Sylow | C5 ⋊ C3×#444 |
208 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,12,13,20,14,21,22,11)(10,15,16,23,18,24,17,19);(9,11,13,12,14,20,22,21)(10,15,17,19,18,24,16,23);(5,6)(7,8)(9,10)(11,19)(12,15)(13,16)(14,18)(17,22)(20,23)(21,24)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10601710, C3×#10599883, #14315779, … |
| maximal normal subgroup of | C3×#10601710, C3×#10599883, #14315779, … |
| maximal quotient of | C3×#10598869, C3×#10598877, C3×#10598870, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3809);