Finite Group DatabasebetaFinite Group Databasebeta| order | 11766 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C53 · Schur multiplier (H2) = C1 |
| direct product | C2×C53×C37⋊C3 |
| unambiguous semidirect product | (C2×C37)⋊(C3×C53) |
| unambiguous semidirect product | (C2×C37×C53)⋊C3 |
| Fitting, socle, Hall | C2×C37×C53 ⋊ C3 |
| derived, Sylow | C37 ⋊ C2×C3×C53 |
| Hall | C37×C53 ⋊ C2×C3 |
| Hall | C2×C37 ⋊ C3×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C53 | C37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C2×C3×C53 |
| Frattini | C1 | G |
| Fitting, socle | C2×C37×C53 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C53 | |
16 conjugacy classes of subgroups.
1590 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C53×C37⋊C3, C37⋊C3×Dic53, C53×Dic37⋊C3, … |
| maximal normal subgroup of | C4×C53×C37⋊C3, C37⋊C3×Dic53, C53×Dic37⋊C3, … |
| maximal quotient of | C4×C53×C37⋊C3, C22×C53×C37⋊C3, C2×C53×#66524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11766, 2);