Finite Group DatabasebetaFinite Group Databasebeta| order | 17238 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C17 · Schur multiplier (H2) = C1 |
| direct product | C13×C17×D39 |
| unambiguous semidirect product | C3⋊(C13×C17×D13) |
| unambiguous semidirect product | C13⋊(D3×C13×C17) |
| Fitting, socle, Hall | C3×C132×C17 ⋊ C2 |
| derived | C3×C13 ⋊ C2×C13×C17 |
| Hall | C132×C17 ⋊ D3 |
| Hall | C3×C132 ⋊ C2×C17 |
| Sylow | C132 ⋊ D3×C17 |
| Hall | C3×C17 ⋊ C13×D13 |
| Sylow | C3 ⋊ C13×C17×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C17 | D39 |
| commutator, cosocle, hypocenter | C3×C13 | C2×C13×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C132×C17 | C2 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C13×C17 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1326 |
4641 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D17×D39, D3×C13×C17×D13, C13×D39⋊D17, … |
| maximal normal subgroup of | C13×D17×D39, D3×C13×C17×D13, C13×D39⋊D17, … |
| maximal quotient of | C13×C17×Dic39, C2×C13×C17×D39 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17238, 39);