Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | D3×D5⋊C16 |
| unambiguous semidirect product | D5⋊(D3×C16) |
| unambiguous semidirect product | (D3×D5)⋊C16 |
| derived, Hall | C3×C5 ⋊ C22×C16 |
| Sylow | C5 ⋊ C2×D3×C16 |
| Sylow | C3 ⋊ C2×D5⋊C16 |
196 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C16×AGL(1,𝔽5), D3×#64844, #14312697, … |
| maximal normal subgroup of | D3×C16×AGL(1,𝔽5), D3×#64844, #14312697, … |
| maximal quotient of | D3×#64885, #14312537, Dic3×D5⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5836);