Finite Group DatabasebetaFinite Group Databasebeta| order | 8686 |
| isoclinism | isoclinic class of D43 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C101 · Schur multiplier (H2) = C1 |
| direct product | D43×C101 |
| unambiguous semidirect product | C43⋊(C2×C101) |
| Fitting, socle, Hall | C43×C101 ⋊ C2 |
| derived, Sylow | C43 ⋊ C2×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | D43 |
| commutator, hypocenter | C43 | C2×C101 |
| Frattini | C1 | G |
| Fitting, socle | C43×C101 | C2 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C101 | |
8 conjugacy classes of subgroups.
2323 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×D101, C2×D43×C101, C3×D43×C101, … |
| maximal normal subgroup of | D43×D101, C2×D43×C101, C3×D43×C101, … |
| maximal quotient of | C101×Dic43, C2×D43×C101, C3×D43×C101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8686, 1);