Finite Group DatabasebetaFinite Group Databasebeta| order | 5340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic445 |
| derived, Hall | C5×C89 ⋊ C3×C4 |
| Hall | C3×C5×C89 ⋊ C4 |
| Hall | C3×C89 ⋊ Dic5 |
| Sylow | C89 ⋊ C3×Dic5 |
| Hall | C3×C5 ⋊ Dic89 |
| Sylow | C5 ⋊ C3×Dic89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D445 |
| commutator, hypocenter | C5×C89 | C3×C4 |
| Frattini | C2 | C3×D445 |
| Fitting, socle | C2×C3×C5×C89 | C2 |
| LCS | G ▷ C5×C89 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
1344 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic445, C32×Dic445, C3×Dic1335, … |
| maximal normal subgroup of | C9×Dic445, C32×Dic445, C3×C5×Dic445, … |
| maximal quotient of | C9×Dic445, C32×Dic445, C3×Dic1335, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5340, 4);