Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C3×#4007 |
| unambiguous semidirect product | D5⋊(C3×#102) |
| Fitting | C2×C3×C5×D4 ⋊ C4 |
| Hall | C3×C5 ⋊ C2×#102 |
| Sylow | C5 ⋊ C2×C3×#102 |
404 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×#4007, C3×AGL(1,𝔽5)×#102, Dic3×#4007, … |
| maximal normal subgroup of | C3×C4×#4007, C3×AGL(1,𝔽5)×#102, Dic3×#4007, … |
| maximal quotient of | C2×C3×D4⋊#170, C2×C3×#64871, C3×D5⋊(D4⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6494);