Finite Group DatabasebetaFinite Group Databasebeta| order | 17214 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D453 |
| unambiguous semidirect product | C3⋊(C19×D151) |
| unambiguous semidirect product | C151⋊(D3×C19) |
| Fitting, socle, Hall | C3×C19×C151 ⋊ C2 |
| derived, Hall | C3×C151 ⋊ C2×C19 |
| Hall | C19×C151 ⋊ D3 |
| Sylow | C151 ⋊ D3×C19 |
| Hall | C3×C19 ⋊ D151 |
| Sylow | C3 ⋊ C19×D151 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D453 |
| commutator, cosocle, hypocenter | C3×C151 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C151 | C2 |
| LCS | G ▷ C3×C151 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8607 |
4332 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C19×D151, D19×D453, D57⋊D151, … |
| maximal normal subgroup of | D3×C19×D151, D19×D453, D57⋊D151, … |
| maximal quotient of | C19×Dic453, C2×C19×D453 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17214, 10);