Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of D5×C3⋊AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | D5×C3⋊AGL(1,ℤ/9) |
| unambiguous semidirect product | (C3×D5)⋊AGL(1,ℤ/9) |
| Fitting, Hall | C3×C5×3−1+2 ⋊ C22 |
| derived | C3×C5×C9 ⋊ C22×C3 |
| Sylow | C3×3−1+2 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×C3⋊AGL(1,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C5×C9 | C22×C3 |
| Frattini | C3 | C3×D5×C3⋊D3 |
| Fitting | C3×C5×3−1+2 | C22 |
| socle | C32×C5 | C2×C3×D3 |
| LCS | G ▷ C3×C5×C9 | |
| UCS | C1 | |
236 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 135 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 309);