Finite Group DatabasebetaFinite Group Databasebeta| order | 6622 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C43 · Schur multiplier (H2) = C1 |
| direct product | C7×D11×C43 |
| unambiguous semidirect product | C11⋊(C2×C7×C43) |
| Fitting, socle, Hall | C7×C11×C43 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C7×C43 |
| Hall | C11×C43 ⋊ C2×C7 |
| Hall | C7×C11 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C43 | D11 |
| commutator, hypocenter | C11 | C2×C7×C43 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C43 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C7×C43 | |
16 conjugacy classes of subgroups.
2107 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×D11×C43, C7×C43×D55, C7×C43×AGL(1,𝔽11) |
| maximal normal subgroup of | C5×C7×D11×C43, C7×C43×AGL(1,𝔽11) |
| maximal quotient of | C5×C7×D11×C43, C7×C43×D55 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6622, 4);