Finite Group DatabasebetaFinite Group Databasebeta| order | 6740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D337 |
| unambiguous semidirect product | (D5×C337)⋊C2 |
| unambiguous semidirect product | (C5×D337)⋊C2 |
| unambiguous semidirect product | D1685⋊C2 |
| Fitting, socle, derived, Hall | C5×C337 ⋊ C22 |
| Sylow | C337 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D337 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C337 | C22 |
| LCS | G ▷ C5×C337 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
680 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D337⋊C3, C3×D5×D337, D15×D337, … |
| maximal normal subgroup of | D5×D337⋊C3, C3×D5×D337, C5×D5×D337 |
| maximal quotient of | C3×D5×D337, D15×D337, D5×D1011, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6740, 12);