Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of D15⋊(C3⋊(C3⋊D3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C33 |
| unambiguous semidirect product | D15⋊(C3⋊(C3⋊D3)) |
| Fitting, socle, derived, Hall | C34×C5 ⋊ C22 |
| Sylow | C34 ⋊ C2×D5 |
| Sylow | C5 ⋊ D3×C3⋊(C3⋊D3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C34×C5 | C22 |
| LCS | G ▷ C34×C5 | |
| UCS | C1 | |
872 conjugacy classes of subgroups.
| transitive degree | μt(G) = 270 |
Polycyclic presentation:
2^2,3^4,5|c^a=c^2,d^a=d^2,e^a=e^2,g^a=g^4,c^b=c^2,d^b=d^2,e^b=e^2,f^b=f^2129 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 460);