Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of D5×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| Fitting, Hall | C5×C9⋊C9 ⋊ C22 |
| derived | C5×C9 ⋊ C22×C9 |
| Sylow | C9⋊C9 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D9⋊C9 |
106 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 106 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 | D5×#92265, AGL(1,𝔽5)×D9⋊C9, D5×AGL(1,ℤ/27) |
| maximal normal subgroup of | D5×#92265, AGL(1,𝔽5)×D9⋊C9 |
| maximal quotient of | D5×AGL(1,ℤ/27) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 107);