Finite Group DatabasebetaFinite Group Databasebeta| order | 5340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#13184069 |
| Fitting, socle, derived, Hall | C3×C5×C89 ⋊ C4 |
| Hall | C5×C89 ⋊ Dic3 |
| Hall | C3×C89 ⋊ AGL(1,𝔽5) |
| Sylow | C89 ⋊ ΓL(1,𝔽16) |
| Hall | C3×C5 ⋊ Dic89 |
| Sylow | C5 ⋊ Dic267 |
| Sylow | C3 ⋊ #13184069 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C89 | C4 |
| LCS | G ▷ C3×C5×C89 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,89|a^2=b,c^a=c^2,d^a=d^2,e^a=e^88,d^b=d^4537 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5340, 22);