Finite Group DatabasebetaFinite Group Databasebeta| order | 11766 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C1 |
| direct product | C3×C37×D53 |
| unambiguous semidirect product | C53⋊(C2×C3×C37) |
| Fitting, socle, Hall | C3×C37×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C2×C3×C37 |
| Hall | C37×C53 ⋊ C2×C3 |
| Hall | C3×C53 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C37 | D53 |
| commutator, cosocle, hypocenter | C53 | C2×C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C3×C37×C53 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C3×C37 | |
16 conjugacy classes of subgroups.
3108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C37×#6157, C3×#21463228, C3×D37×D53, … |
| maximal normal subgroup of | C3×C37×#6157, C3×#21463228, C3×D37×D53, … |
| maximal quotient of | C3×C37×Dic53, C2×C3×C37×D53, C9×C37×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11766, 3);