Finite Group DatabasebetaFinite Group Databasebeta| order | 6622 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | D11×C43⋊C7 |
| unambiguous semidirect product | C11⋊(C2×C43⋊C7) |
| unambiguous semidirect product | (D11×C43)⋊C7 |
| Fitting, socle, derived, Hall | C11×C43 ⋊ C2×C7 |
| Hall | C11×C43⋊C7 ⋊ C2 |
| Hall | D11×C43 ⋊ C7 |
| Sylow | C43 ⋊ C7×D11 |
| Sylow | C11 ⋊ C2×C43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C43 | C2×C7 |
| LCS | G ▷ C11×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
91 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D11×C43⋊C7, D55×C43⋊C7, AGL(1,𝔽11)×C43⋊C7 |
| maximal normal subgroup of | C5×D11×C43⋊C7, AGL(1,𝔽11)×C43⋊C7 |
| maximal quotient of | C5×D11×C43⋊C7, D55×C43⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6622, 11);