Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65157 |
| Fitting | C3×C5×#106 ⋊ C2 |
| Hall | C3×C5 ⋊ #470 |
| Sylow | C5 ⋊ C3×#470 |
220 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 82 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)(15,22)(17,24)(18,25)(21,26)(23,28);(13,15,17,22,16,23,24,28)(14,18,20,26,19,21,27,25);(5,6)(7,8)(10,12)(13,14)(15,21)(16,19)(17,20)(18,23)(22,25)(24,27)(26,28)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598600, #14278014, C3×#10598602, … |
| maximal normal subgroup of | C3×#10598600, #14278014, C3×#10598602, … |
| maximal quotient of | C3×#10599334, C3×#10599344, C3×#10599336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3960);