Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C4 |
| direct product | C3×#64979 |
| Fitting | C3×C4×C5×C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #433 |
| Sylow | C5 ⋊ C3×#433 |
192 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 192 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) = 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)(13,16)(17,19,20,25,21,26,27,31)(18,23,24,30,22,28,29,32);(9,11,12,15)(10,13,14,16)(18,22)(23,28)(24,29)(30,32);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(17,18)(19,23)(20,24)(21,22)(25,30)(26,28)(27,29)(31,32)276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×#433, C2×C3×#64979, #14413845, … |
| maximal normal subgroup of | C3×D5×#433, C2×C3×#64979, #14413845, … |
| maximal quotient of | C3×#10600544, C3×#10600546, C3×#10600548, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3782);