Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | D185⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C5×C37 ⋊ C22 |
| Hall | C32×C37 ⋊ C2×D5 |
| Hall | C5×C37 ⋊ C2×C3⋊D3 |
| Hall | C32×C5 ⋊ C2×D37 |
| Sylow | C37 ⋊ D5×C3⋊D3 |
| Sylow | C32 ⋊ D5×D37 |
| Sylow | C5 ⋊ C3⋊D3×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C37 | C22 |
| LCS | G ▷ C32×C5×C37 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5,37|e^a=e^4,f^a=f^36,c^b=c^2,d^b=d^2,e^b=e^4456 conjugacy classes — view the full character table.
| maximal subgroup of | D925⋊(C3⋊D3), C5×D185⋊(C3⋊D3), D185⋊(C3⋊D15), … |
| maximal normal subgroup of | C5×D185⋊(C3⋊D3) |
| maximal quotient of | D925⋊(C3⋊D3), C5×D185⋊(C3⋊D3), D185⋊(C3⋊D15), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 147);