Finite Group DatabasebetaFinite Group Databasebeta| order | 6580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D5×D47 |
| unambiguous semidirect product | (D5×C47)⋊(C2×C7) |
| unambiguous semidirect product | (C5×D47)⋊(C2×C7) |
| unambiguous semidirect product | D235⋊(C2×C7) |
| Fitting, socle, Hall | C5×C7×C47 ⋊ C22 |
| derived, Hall | C5×C47 ⋊ C22×C7 |
| Hall | C7×C47 ⋊ C2×D5 |
| Sylow | C47 ⋊ C2×C7×D5 |
| Hall | C5×C7 ⋊ C2×D47 |
| Sylow | C5 ⋊ C2×C7×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D5×D47 |
| commutator, hypocenter | C5×C47 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C47 | C22 |
| LCS | G ▷ C5×C47 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
700 conjugacy classes — view the full character table.
| maximal subgroup of | D5×ΓL(1,𝔽8)×D47, C3×C7×D5×D47, C7×D15×D47, … |
| maximal normal subgroup of | D5×ΓL(1,𝔽8)×D47, C3×C7×D5×D47, C5×C7×D5×D47 |
| maximal quotient of | C3×C7×D5×D47, C7×D15×D47, C7×D5×D141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6580, 15);