Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of D5×(C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | D5×(C3⋊D3)⋊C9 |
| unambiguous semidirect product | (D5×C3⋊D3)⋊C9 |
| Fitting, Hall | C5×C32⋊C9 ⋊ C22 |
| derived | C32×C5 ⋊ C22×C9 |
| Sylow | C32⋊C9 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×(C3⋊D3)⋊C9 |
134 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 90 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×(C3⋊D3)⋊C9, D5×((C3⋊D3)⋊C9)⋊C2, #72247379, … |
| maximal normal subgroup of | AGL(1,𝔽5)×(C3⋊D3)⋊C9, D5×((C3⋊D3)⋊C9)⋊C2, #72247379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 105);