Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of D3×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×D3×D9 |
| Fitting, Hall | C32×C5×C9 ⋊ C22 |
| derived | C3×C9 ⋊ C22×C3×C5 |
| Sylow | C32×C9 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D3×D9 |
| commutator, cosocle, hypocenter | C3×C9 | C22×C3×C5 |
| Frattini | C3 | C3×C5×D32 |
| Fitting | C32×C5×C9 | C22 |
| socle | C33×C5 | C2×D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C3×C5 | |
172 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 180 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 312);