Finite Group DatabasebetaFinite Group Databasebeta| order | 5340 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C89 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic5×C89 |
| derived, Sylow | C5 ⋊ C3×C4×C89 |
| Hall | C3×C5×C89 ⋊ C4 |
| Hall | C5×C89 ⋊ C3×C4 |
| Hall | C3×C5 ⋊ C4×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C89 | D5 |
| commutator, hypocenter | C5 | C3×C4×C89 |
| Frattini | C2 | C3×D5×C89 |
| Fitting, socle | C2×C3×C5×C89 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C3×C89 | |
24 conjugacy classes of subgroups.
2136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic5×C89, C32×Dic5×C89, C3×Dic15×C89, … |
| maximal normal subgroup of | C9×Dic5×C89, C32×Dic5×C89, C3×C5×Dic5×C89, … |
| maximal quotient of | C9×Dic5×C89, C32×Dic5×C89, C3×Dic15×C89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5340, 3);