Finite Group DatabasebetaFinite Group Databasebeta| order | 17238 |
| isoclinism | isoclinic class of D221 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×D221 |
| unambiguous semidirect product | C17⋊(C3×C13×D13) |
| Fitting, socle, Hall | C3×C132×C17 ⋊ C2 |
| derived | C13×C17 ⋊ C2×C3×C13 |
| Hall | C132×C17 ⋊ C2×C3 |
| Hall | C3×C132 ⋊ D17 |
| Sylow | C132 ⋊ C3×D17 |
| Hall | C3×C17 ⋊ C13×D13 |
| Sylow | C17 ⋊ C3×C13×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | D221 |
| commutator, cosocle, hypocenter | C13×C17 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C132×C17 | C2 |
| LCS | G ▷ C13×C17 | |
| UCS | C1 ◁ C3×C13 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1326 |
4368 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C13×D13×D17, C3×C13×#11725130, C3×C13×#11725131, … |
| maximal normal subgroup of | C3×C13×D13×D17, C3×C13×#11725130, C3×C13×#11725131, … |
| maximal quotient of | C3×C13×Dic221, C2×C3×C13×D221 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17238, 44);