Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | D5×C3⋊D111 |
| unambiguous semidirect product | (C3×D5)⋊D111 |
| unambiguous semidirect product | (D5×C37)⋊(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 ⋊ C2×C3⋊D111 |
| 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.
672 conjugacy classes — view the full character table.
| maximal subgroup of | D25×C3⋊D111, C5×D5×C3⋊D111, D5×C3⋊D555, … |
| maximal normal subgroup of | C5×D5×C3⋊D111 |
| maximal quotient of | D25×C3⋊D111, C5×D5×C3⋊D111, D5×C3⋊D555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 145);