Finite Group DatabasebetaFinite Group Databasebeta| order | 11766 |
| isoclinism | isoclinic class of D111 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×D111 |
| unambiguous semidirect product | C3⋊(C53×D37) |
| unambiguous semidirect product | C37⋊(D3×C53) |
| Fitting, socle, Hall | C3×C37×C53 ⋊ C2 |
| derived, Hall | C3×C37 ⋊ C2×C53 |
| Hall | C37×C53 ⋊ D3 |
| Hall | C3×C53 ⋊ D37 |
| Sylow | C37 ⋊ D3×C53 |
| Sylow | C3 ⋊ C53×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D111 |
| commutator, cosocle, hypocenter | C3×C37 | C2×C53 |
| Frattini | C1 | G |
| Fitting, socle | C3×C37×C53 | C2 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C53 | |
16 conjugacy classes of subgroups.
3021 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×D111, D3×C53×D37, D111⋊D53, … |
| maximal normal subgroup of | D53×D111, D3×C53×D37, D111⋊D53, … |
| maximal quotient of | C53×Dic111, C2×C53×D111, C53×D333, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11766, 8);