Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| isoclinism | isoclinic class of C3⋊(C3⋊D9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C33 |
| direct product | C5×C3⋊(C3⋊D9) |
| unambiguous semidirect product | C3⋊(C5×C3⋊D9) |
| unambiguous semidirect product | C9⋊(C5×C3⋊D3) |
| Fitting, Hall | C32×C5×C9 ⋊ C2 |
| derived, Sylow | C32×C9 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊(C3⋊D9) |
| commutator, cosocle, hypocenter | C32×C9 | C2×C5 |
| Frattini | C3 | C5×C3⋊(C3⋊D3) |
| Fitting | C32×C5×C9 | C2 |
| socle | C33×C5 | D3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C5 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 405 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C3⋊(C3⋊D9), C5×D3×C3⋊D9, C5×D9×C3⋊D3, … |
| maximal normal subgroup of | D5×C3⋊(C3⋊D9), C5×D3×C3⋊D9, C5×D9×C3⋊D3, … |
| maximal quotient of | C5×C3⋊(C3⋊Dic9), C2×C5×C3⋊(C3⋊D9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 93);