Finite Group DatabasebetaFinite Group Databasebeta| order | 5220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D435 |
| unambiguous semidirect product | (C3×D3)⋊D145 |
| unambiguous semidirect product | (C5×D3)⋊D87 |
| unambiguous semidirect product | (D3×C29)⋊D15 |
| Fitting, socle, derived, Hall | C32×C5×C29 ⋊ C22 |
| Hall | C32×C29 ⋊ C2×D5 |
| Hall | C5×C29 ⋊ D32 |
| Hall | C32×C5 ⋊ C2×D29 |
| Sylow | C29 ⋊ D3×D15 |
| Sylow | C32 ⋊ C2×D145 |
| Sylow | C5 ⋊ D3×D87 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C29 | C22 |
| LCS | G ▷ C32×C5×C29 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
657 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D2175, C5×D3×D435, D15×D435, … |
| maximal normal subgroup of | C5×D3×D435, D3×C3⋊(C5⋊(D29⋊C7)), D3×C7×D435 |
| maximal quotient of | D3×D2175, C5×D3×D435, D15×D435, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5220, 85);