Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #19153613⋊C3 |
| Fitting, socle, derived, Hall | C5×C172 ⋊ C3×C4 |
| Hall | #19153613 ⋊ C3 |
| Hall | C5×C172⋊C3 ⋊ C4 |
| Hall | C172⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C172 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ #11923883⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C172 | C3×C4 |
| prime radical | C5⋊((C17⋊D17)⋊C3) | C2 |
| cosocle | C5⋊(C17⋊D17) | C2×C3 |
| LCS | G ▷ C5×C172 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 255 |
Polycyclic presentation:
2,3,2,5,17^2|a^2=c,d^a=d^2,e^a=e^4,f^a=f^4,e^b=e^2f^16,f^b=e^7f^14,d^c=d^4,e^c=e^16,f^c=f^16135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 61);