Finite Group DatabasebetaFinite Group Databasebeta| order | 8502 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C109 · Schur multiplier (H2) = C1 |
| direct product | D39×C109 |
| unambiguous semidirect product | C3⋊(D13×C109) |
| unambiguous semidirect product | C13⋊(D3×C109) |
| Fitting, socle, Hall | C3×C13×C109 ⋊ C2 |
| derived, Hall | C3×C13 ⋊ C2×C109 |
| Hall | C13×C109 ⋊ D3 |
| Hall | C3×C109 ⋊ D13 |
| Sylow | C13 ⋊ D3×C109 |
| Sylow | C3 ⋊ D13×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C109 | D39 |
| commutator, hypocenter | C3×C13 | C2×C109 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C109 | C2 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C109 | |
16 conjugacy classes of subgroups.
2289 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D39×D109, D3×D13×C109, D39⋊D109, … |
| maximal normal subgroup of | D39×D109, D3×D13×C109, D39⋊D109, … |
| maximal quotient of | C109×Dic39, C2×D39×C109, C109×D117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8502, 11);