Finite Group DatabasebetaFinite Group Databasebeta| order | 6740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#13062438 |
| Fitting, socle, Hall | C5×C337 ⋊ C4 |
| derived, Sylow | C337 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #13062438 |
| commutator, hypocenter | C337 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C337 | C4 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6740, 6);