Finite Group DatabasebetaFinite Group Databasebeta| order | 6162 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C79 · Schur multiplier (H2) = C1 |
| direct product | D39×C79 |
| unambiguous semidirect product | C3⋊(D13×C79) |
| unambiguous semidirect product | C13⋊(D3×C79) |
| Fitting, socle, Hall | C3×C13×C79 ⋊ C2 |
| derived, Hall | C3×C13 ⋊ C2×C79 |
| Hall | C13×C79 ⋊ D3 |
| Hall | C3×C79 ⋊ D13 |
| Sylow | C13 ⋊ D3×C79 |
| Sylow | C3 ⋊ D13×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | D39 |
| commutator, hypocenter | C3×C13 | C2×C79 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C79 | C2 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C79 | |
16 conjugacy classes of subgroups.
1659 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D39×D79, D3×D13×C79, D39⋊D79, … |
| maximal normal subgroup of | D39×D79, D3×D13×C79, D39⋊D79, … |
| maximal quotient of | C79×Dic39, C2×D39×C79, C79×D117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6162, 13);