Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#65169 |
| Fitting | C3×C5×#107 ⋊ C2 |
| Hall | C3×C5 ⋊ #427 |
| Sylow | C5 ⋊ C3×#427 |
228 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,7,8,6)(9,10,11,12)(14,19)(15,21)(16,24)(18,25)(22,23)(26,28);(13,15,16,22,17,23,24,21)(14,18,20,25,19,26,27,28);(5,6)(7,8)(13,14)(15,18)(16,20)(17,19)(21,28)(22,25)(23,26)(24,27)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598620, #14278858, C3×#10598621, … |
| maximal normal subgroup of | C3×#10598620, #14278858, C3×#10598621, … |
| maximal quotient of | C3×#10599360, C3×#10599363, C3×#10599366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3972);