Finite Group DatabasebetaFinite Group Databasebeta| order | 6580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D35×D47 |
| unambiguous semidirect product | (C5×D47)⋊D7 |
| unambiguous semidirect product | (C7×D47)⋊D5 |
| Fitting, socle, derived, Hall | C5×C7×C47 ⋊ C22 |
| Hall | C7×C47 ⋊ C2×D5 |
| Hall | C5×C47 ⋊ C2×D7 |
| Sylow | C47 ⋊ C2×D35 |
| Hall | C5×C7 ⋊ C2×D47 |
| Sylow | C7 ⋊ D5×D47 |
| Sylow | C5 ⋊ D7×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C47 | C22 |
| LCS | G ▷ C5×C7×C47 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
475 conjugacy classes — view the full character table.
| maximal subgroup of | D47×C5⋊AGL(1,𝔽7), C3×D35×D47, D47×D105, … |
| maximal normal subgroup of | D47×C5⋊AGL(1,𝔽7), C3×D35×D47, C5×D35×D47 |
| maximal quotient of | C3×D35×D47, D47×D105, D35×D141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6580, 16);