Finite Group DatabasebetaFinite Group Databasebeta| order | 5340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊D89 |
| unambiguous semidirect product | D267⋊D5 |
| unambiguous semidirect product | D445⋊D3 |
| Fitting, socle, derived, Hall | C3×C5×C89 ⋊ C22 |
| Hall | C5×C89 ⋊ C2×D3 |
| Hall | C3×C89 ⋊ C2×D5 |
| Sylow | C89 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×D89 |
| Sylow | C5 ⋊ D3×D89 |
| Sylow | C3 ⋊ D5×D89 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C89 | C22 |
| LCS | G ▷ C3×C5×C89 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,89|d^a=d^4,e^a=e^88,c^b=c^2,d^b=d^4408 conjugacy classes — view the full character table.
| maximal subgroup of | D45⋊D89, C3×D15⋊D89, D445⋊(C3⋊D3), … |
| maximal normal subgroup of | C3×D15⋊D89, C5×D15⋊D89, C7×D15⋊D89 |
| maximal quotient of | D45⋊D89, C3×D15⋊D89, D445⋊(C3⋊D3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5340, 28);