Finite Group DatabasebetaFinite Group Databasebeta| order | 5340 |
| automorphism | Aut(G) order 1879680 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2670 |
| direct product | C2×D1335 |
| unambiguous semidirect product | (C2×C3)⋊D445 |
| unambiguous semidirect product | (C2×C5)⋊D267 |
| unambiguous semidirect product | (C2×C89)⋊D15 |
| Fitting, socle | C2×C3×C5×C89 ⋊ C2 |
| derived, Hall | C3×C5×C89 ⋊ C22 |
| Hall | C5×C89 ⋊ C2×D3 |
| Hall | C3×C89 ⋊ C2×D5 |
| Sylow | C89 ⋊ C2×D15 |
| Hall | C3×C5 ⋊ C2×D89 |
| Sylow | C5 ⋊ C2×D267 |
| Sylow | C3 ⋊ C2×D445 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1335 |
| commutator, hypocenter | C3×C5×C89 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C89 | C2 |
| LCS | G ▷ C3×C5×C89 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
1338 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4005, D3×D1335, C2×C3⋊D1335, … |
| maximal normal subgroup of | C2×C3×D1335, C2×C5×D1335, C2×C7×D1335, … |
| maximal quotient of | C2×D4005, D3×D1335, C2×C3⋊D1335, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5340, 30);