Finite Group DatabasebetaFinite Group Databasebeta| order | 6708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C22×#13131976 |
| Fitting, socle, Hall | C22×C13×C43 ⋊ C3 |
| derived, Hall | C13×C43 ⋊ C22×C3 |
| Hall | C22×C43 ⋊ C13⋊C3 |
| Hall | C22×C13 ⋊ C43⋊C3 |
| Sylow | C43 ⋊ C22×C13⋊C3 |
| Sylow | C13 ⋊ C22×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #13131976 |
| commutator, hypocenter | C13×C43 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C13×C43 | C3 |
| LCS | G ▷ C13×C43 | |
| UCS | C1 ◁ C22 | |
40 conjugacy classes of subgroups.
756 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6708, 66);