Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#66065 |
| Fitting | C3×C5×C4⋊Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #541 |
| Sylow | C5 ⋊ C3×#541 |
384 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 190 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 32 points:
(1,2,3)(4,5,7,8,6)(9,11,12,15)(10,14,13,16)(18,24)(22,30)(23,32)(29,31);(10,13)(11,15)(17,20,21,28)(18,23,24,32)(19,25,26,27)(22,29,30,31);(17,19,21,26)(18,22,24,30)(20,27,28,25)(23,31,32,29);(5,6)(7,8)(9,10)(11,14)(12,13)(15,16)(17,18)(19,22)(20,23)(21,24)(25,29)(26,30)(27,31)(28,32)150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10612143, C3×#10612191, #14436243, … |
| maximal normal subgroup of | C3×#10612143, C3×#10612191, #14436243, … |
| maximal quotient of | C3×#10606089, C3×#10608214, C3×#10608342, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9937);