Finite Group DatabasebetaFinite Group Databasebeta| order | 5340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic267 |
| unambiguous semidirect product | C3⋊(C5×Dic89) |
| derived, Hall | C3×C89 ⋊ C4×C5 |
| Hall | C3×C5×C89 ⋊ C4 |
| Hall | C5×C89 ⋊ Dic3 |
| Sylow | C89 ⋊ C5×Dic3 |
| Hall | C3×C5 ⋊ Dic89 |
| Sylow | C3 ⋊ C5×Dic89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D267 |
| commutator, hypocenter | C3×C89 | C4×C5 |
| Frattini | C2 | C5×D267 |
| Fitting, socle | C2×C3×C5×C89 | C2 |
| LCS | G ▷ C3×C89 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
1350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×Dic801, C3×C5×Dic267, C5×C3⋊Dic267, … |
| maximal normal subgroup of | C3×C5×Dic267, C25×Dic267, C52×Dic267, … |
| maximal quotient of | C5×Dic801, C3×C5×Dic267, C5×C3⋊Dic267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5340, 6);