Finite Group DatabasebetaFinite Group Databasebeta| order | 6020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D35×D43 |
| unambiguous semidirect product | (C5×D43)⋊D7 |
| unambiguous semidirect product | (C7×D43)⋊D5 |
| Fitting, socle, derived, Hall | C5×C7×C43 ⋊ C22 |
| Hall | C7×C43 ⋊ C2×D5 |
| Hall | C5×C43 ⋊ C2×D7 |
| Sylow | C43 ⋊ C2×D35 |
| Hall | C5×C7 ⋊ C2×D43 |
| Sylow | C7 ⋊ D5×D43 |
| Sylow | C5 ⋊ D7×D43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C43 | C22 |
| LCS | G ▷ C5×C7×C43 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
437 conjugacy classes — view the full character table.
| maximal subgroup of | #14268588⋊D5, #14268587⋊D5, D43×C5⋊AGL(1,𝔽7), … |
| maximal normal subgroup of | #14268588⋊D5, #14268587⋊D5, D43×C5⋊AGL(1,𝔽7), … |
| maximal quotient of | C3×D35×D43, D43×D105, D35×D129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6020, 27);