Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#65040 |
| Fitting | C3×C5×#101 ⋊ C2 |
| Hall | C3×C5 ⋊ #413 |
| Sylow | C5 ⋊ C3×#413 |
300 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,11,12,18,13,19,21,24)(10,15,16,22,14,17,20,23);(9,10,13,14)(11,17,19,15)(12,20,21,16)(18,22,24,23);(5,6)(7,8)(10,14)(15,17)(16,20)(22,23)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598578, #14279165, C3×#10603932, … |
| maximal normal subgroup of | C3×#10598578, #14279165, C3×#10603932, … |
| maximal quotient of | C3×#10598917, C3×#10598936, C3×#10598919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3843);