Finite Group DatabasebetaFinite Group Databasebeta| order | 8686 |
| isoclinism | isoclinic class of D101 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D101 |
| unambiguous semidirect product | C101⋊(C2×C43) |
| Fitting, socle, Hall | C43×C101 ⋊ C2 |
| derived, Sylow | C101 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D101 |
| commutator, hypocenter | C101 | C2×C43 |
| Frattini | C1 | G |
| Fitting, socle | C43×C101 | C2 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C43 | |
8 conjugacy classes of subgroups.
2236 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#87938, C43⋊#87938, D43×D101, … |
| maximal normal subgroup of | C43×#87938, C43⋊#87938, D43×D101, … |
| maximal quotient of | C43×Dic101, C2×C43×D101, C3×C43×D101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8686, 2);