Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#64697 |
| Fitting | C3×C5×#101 ⋊ C2 |
| Hall | C3×C5 ⋊ #355 |
| Sylow | C5 ⋊ C3×#355 |
128 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 42 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 — 2 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,10,11,15,13,16,18,24)(12,14,20,21,19,22,17,23);(5,6)(7,8)(10,14)(12,19)(15,23)(16,22)(17,20)(21,24)105 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#355, C2×C3×#64697, #14313574, … |
| maximal normal subgroup of | C3×D5×#355, C2×C3×#64697, #14313574, … |
| maximal quotient of | C3×#10597945, C3×#10597943, C3×#10597984, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 249);