Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#10625191⋊C3 |
| unambiguous semidirect product | #10625191⋊C32 |
| unambiguous semidirect product | (C3×#10625191)⋊C3 |
| Fitting, socle | C3×C5×C37 ⋊ C3×C4 |
| derived, Hall | C5×C37 ⋊ C32×C4 |
| Hall | C3×C5×C37⋊C3 ⋊ C4 |
| Hall | #10625191 ⋊ C32 |
| Hall | C3×C37⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C37 ⋊ C32×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3×#3866⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10625191⋊C3 |
| commutator, hypocenter | C5×C37 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C37 | C3×C4 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#16814854⋊C3, C3×C5×#10625191⋊C3, C3×#16814884⋊C3, … |
| maximal normal subgroup of | C3×C5×#10625191⋊C3 |
| maximal quotient of | C3×#16814854⋊C3, C3×C5×#10625191⋊C3, C3×#16814884⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 89);