Finite Group DatabasebetaFinite Group Databasebeta| order | 6580 |
| isoclinism | isoclinic class of D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×Dic35 |
| unambiguous semidirect product | C7⋊(Dic5×C47) |
| derived, Hall | C5×C7 ⋊ C4×C47 |
| Hall | C5×C7×C47 ⋊ C4 |
| Hall | C7×C47 ⋊ Dic5 |
| Hall | C5×C47 ⋊ Dic7 |
| Sylow | C7 ⋊ Dic5×C47 |
| Sylow | C5 ⋊ Dic7×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C47 | D35 |
| commutator, hypocenter | C5×C7 | C4×C47 |
| Frattini | C2 | C47×D35 |
| Fitting, socle | C2×C5×C7×C47 | C2 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C2×C47 | |
24 conjugacy classes of subgroups.
1786 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C47×Dic35, C47×Dic105, C47×ΓL(1,𝔽8)⋊Dic5, … |
| maximal normal subgroup of | C3×C47×Dic35, C47×ΓL(1,𝔽8)⋊Dic5, C5×C47×Dic35 |
| maximal quotient of | C3×C47×Dic35, C47×Dic105, C47×Dic175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6580, 7);