Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65256 |
| Fitting | C2×C3×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #480 |
| Sylow | C5 ⋊ C3×#480 |
228 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 228 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) = 24 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,11,12,15)(10,14,13,16)(18,21)(19,24)(22,23);(10,13)(14,16);(5,6)(7,8)(9,10)(11,14)(12,13)(15,16)(17,18)(19,21)(20,23)(22,24)177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10601957, C3×#10600501, #14288255, … |
| maximal normal subgroup of | C3×#10601957, C3×#10600501, #14288255, … |
| maximal quotient of | C3×#10602346, C3×#10602348, C3×#10602353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4059);