Finite Group DatabasebetaFinite Group Databasebeta| order | 6020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C43 · Schur multiplier (H2) = C2 |
| direct product | D5×D7×C43 |
| unambiguous semidirect product | (C7×D5)⋊(C2×C43) |
| unambiguous semidirect product | (C5×D7)⋊(C2×C43) |
| unambiguous semidirect product | D35⋊(C2×C43) |
| Fitting, socle, Hall | C5×C7×C43 ⋊ C22 |
| derived, Hall | C5×C7 ⋊ C22×C43 |
| Hall | C7×C43 ⋊ C2×D5 |
| Hall | C5×C43 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D5×C43 |
| Sylow | C5 ⋊ C2×D7×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D5×D7 |
| commutator, hypocenter | C5×C7 | C22×C43 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C43 | C22 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C43 | |
40 conjugacy classes of subgroups.
860 conjugacy classes — view the full character table.
| maximal subgroup of | D5×AGL(1,𝔽7)×C43, D5×#14268592, D5×#14268591, … |
| maximal normal subgroup of | D5×AGL(1,𝔽7)×C43, D5×#14268592, D5×#14268591, … |
| maximal quotient of | C3×D5×D7×C43, D7×D15×C43, D5×D21×C43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6020, 28);