Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#19153589 |
| Fitting, derived, Hall | C3×C5×C289 ⋊ C4 |
| Hall | C5×C289 ⋊ Dic3 |
| Hall | C3×C289 ⋊ AGL(1,𝔽5) |
| Sylow | C289 ⋊ ΓL(1,𝔽16) |
| Hall | C3×C5 ⋊ Dic289 |
| Sylow | C5 ⋊ Dic867 |
| Sylow | C3 ⋊ #19153589 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C5×C289 | C4 |
| Frattini | C17 | C3⋊#66774 |
| socle | C3×C5×C17 | Dic17 |
| prime radical | C3×D5×C17 | D17 |
| cosocle | C3×D5×C289 | C2 |
| LCS | G ▷ C3×C5×C289 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4335 |
Polycyclic presentation:
2^2,3,5,17^2|a^2=b,e^17=f^16,c^a=c^2,d^a=d^2,e^a=e^16f,f^a=f^16,d^b=d^41737 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 20);