Finite Group DatabasebetaFinite Group Databasebeta| order | 7766 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D353 |
| Fitting, socle, Hall | C11×C353 ⋊ C2 |
| derived, Sylow | C353 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D353 |
| commutator, hypocenter | C353 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C353 | C2 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
1958 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#13083443, C11⋊#13083443, D11×D353, … |
| maximal normal subgroup of | C11×#13083443, C11⋊#13083443, D11×D353, … |
| maximal quotient of | C11×Dic353, C2×C11×D353, C3×C11×D353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7766, 4);