Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#65012 |
| Hall | C3×C5 ⋊ #485 |
| Sylow | C5 ⋊ C3×#485 |
192 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 78 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 — 3 generators on 32 points:
(1,2,3)(4,5,7,8,6)(10,14)(11,15)(17,20,21,28,22,29,19,26)(18,24,23,27,25,31,30,32);(9,11)(10,13)(12,15)(14,16)(17,19,22,21)(18,23,25,30)(20,26,29,28)(24,27,31,32);(5,6)(7,8)(9,10,12,14)(11,13,15,16)(17,18)(19,23)(20,27)(21,30)(22,25)(24,28)(26,31)(29,32)177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#485, C2×C3×#65012, #14431624, … |
| maximal normal subgroup of | C3×D5×#485, C2×C3×#65012, #14431624, … |
| maximal quotient of | C3×#10600719, C3×#10600722, C3×#10600724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3815);