Finite Group DatabasebetaFinite Group Databasebeta| order | 5330 |
| isoclinism | isoclinic class of D205 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D205 |
| unambiguous semidirect product | C5⋊(C13×D41) |
| unambiguous semidirect product | C41⋊(D5×C13) |
| Fitting, socle, Hall | C5×C13×C41 ⋊ C2 |
| derived, Hall | C5×C41 ⋊ C2×C13 |
| Hall | C13×C41 ⋊ D5 |
| Hall | C5×C13 ⋊ D41 |
| Sylow | C41 ⋊ D5×C13 |
| Sylow | C5 ⋊ C13×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D205 |
| commutator, hypocenter | C5×C41 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C41 | C2 |
| LCS | G ▷ C5×C41 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C13×D205, C13×D615, C13⋊C3×D205, … |
| maximal normal subgroup of | C3×C13×D205, C13⋊C3×D205, C13×C5⋊(D41⋊C5), … |
| maximal quotient of | C3×C13×D205, C13×D615, C13×D1025, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5330, 7);