Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #13181892⋊D5 |
| Fitting, socle, Hall | C5×C172 ⋊ C2×D3 |
| derived, Hall | C5×C172⋊C3 ⋊ C22 |
| Hall | C172⋊C3 ⋊ C2×D5 |
| Sylow | C172 ⋊ D3×D5 |
| Sylow | C5 ⋊ #13181892⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C172⋊C3 | C22 |
| Fitting, socle | C5×C172 | C2×D3 |
| LCS | G ▷ C5×C172⋊C3 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 255 |
Polycyclic presentation:
2^2,3,5,17^2|c^a=c^2,d^a=d^4,e^a=e^16,f^a=e^16f,c^b=c^2,f^b=ef^16,e^c=e^2f^12,f^c=e^15f^14204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 65);