Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C81 · Schur multiplier (H2) = C2 |
| direct product | C2×D5×C81 |
| unambiguous semidirect product | C5⋊(C22×C81) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C81) |
| Fitting | C2×C5×C81 ⋊ C2 |
| derived, Sylow | C5 ⋊ C22×C81 |
| Hall | C5×C81 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C81 | D5 |
| commutator, hypocenter | C5 | C22×C81 |
| Frattini | C27 | C2×C3×D5 |
| Fitting | C2×C5×C81 | C2 |
| socle | C2×C3×C5 | C2×C27 |
| prime radical | C2×C3×D5 | C27 |
| cosocle | C5×C27 | C22×C3 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C81 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 810 |
648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 9);