Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C5×D32×C9 |
| unambiguous semidirect product | (C3×D3)⋊(C2×C5×C9) |
| Fitting, Hall | C32×C5×C9 ⋊ C22 |
| derived | C32 ⋊ C22×C5×C9 |
| Sylow | C32×C9 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C9 | D32 |
| commutator, hypocenter | C32 | C22×C5×C9 |
| Frattini | C3 | C3×C5×D32 |
| Fitting | C32×C5×C9 | C22 |
| socle | C33×C5 | C22×C3 |
| prime radical | C3×C5×D32 | C3 |
| cosocle | C33 | C22×C3×C5 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C5×C9 | |
172 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 313);