Finite Group DatabasebetaFinite Group Databasebeta| order | 11786 |
| isoclinism | isoclinic class of D71 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C83 · Schur multiplier (H2) = C1 |
| direct product | C83×D71 |
| unambiguous semidirect product | C71⋊(C2×C83) |
| Fitting, socle, Hall | C71×C83 ⋊ C2 |
| derived, Sylow | C71 ⋊ C2×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C83 | D71 |
| commutator, cosocle, hypocenter | C71 | C2×C83 |
| Frattini | C1 | G |
| Fitting, socle | C71×C83 | C2 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C83 | |
8 conjugacy classes of subgroups.
3071 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D71×D83, C2×C83×D71, C3×C83×D71, … |
| maximal normal subgroup of | D71×D83, C2×C83×D71, C3×C83×D71 |
| maximal quotient of | C83×Dic71, C2×C83×D71, C3×C83×D71, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11786, 1);