Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle, Hall | C22×C5×C37 ⋊ C32 |
| derived, Hall | C22×C37 ⋊ C32×C5 |
| Hall | C5×C37 ⋊ C3×A4 |
| Sylow | C37 ⋊ C3×C5×A4 |
| Hall | C22×C5 ⋊ C3×C37⋊C3 |
| Sylow | C22 ⋊ C3×C5×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | A4×C37⋊C3 |
| commutator, hypocenter | C22×C37 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C37 | C32 |
| LCS | G ▷ C22×C37 | |
| UCS | C1 ◁ C5 | |
56 conjugacy classes of subgroups.
300 conjugacy classes — view the full character table.
| maximal subgroup of | A4×C25×C37⋊C3, C52×A4×C37⋊C3, C5×A5×C37⋊C3 |
| maximal normal subgroup of | A4×C25×C37⋊C3, C52×A4×C37⋊C3 |
| maximal quotient of | A4×C25×C37⋊C3, C52×A4×C37⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 109);