Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of C5⋊(C9⋊D9) |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C9 |
| unambiguous semidirect product | C9⋊Dic45 |
| derived, Hall | C5×C92 ⋊ C4 |
| Sylow | C92 ⋊ Dic5 |
| Sylow | C5 ⋊ C9⋊Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊(C9⋊D9) |
| commutator, hypocenter | C5×C92 | C4 |
| Frattini | C2×C32 | C3⋊D15 |
| Fitting, cosocle | C2×C5×C92 | C2 |
| socle, prime radical | C2×C32×C5 | C3⋊D3 |
| LCS | G ▷ C5×C92 | |
| UCS | C1 ◁ C2 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1620 |
Polycyclic presentation:
2^2,3^2,5,3^2|a^2=b,c^3=g,d^3=f,c^a=c^2g^2,d^a=d^2f^2,e^a=e^4,f^a=f^2,g^a=g^2408 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 55);