Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| direct product | A5×C37⋊C3 |
| unambiguous semidirect product | C37⋊(C3×A5) |
| unambiguous semidirect product | (C37×A5)⋊C3 |
| Fitting, Sylow | C37 ⋊ C3×A5 |
| socle, derived | C37×A5 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C37×A5 | C3 |
| Fitting | C37 | C3×A5 |
| LCS | G ▷ C37×A5 | |
| UCS | C1 | |
42 conjugacy classes of subgroups.
75 conjugacy classes — view the full character table.
| maximal subgroup of | C5×A5×C37⋊C3 |
| maximal normal subgroup of | C5×A5×C37⋊C3 |
| maximal quotient of | C5×A5×C37⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 183);