Finite Group DatabasebetaFinite Group Databasebeta| order | 5330 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C13⋊(D41⋊C5) |
| unambiguous semidirect product | (C41⋊C5)⋊D13 |
| unambiguous semidirect product | D533⋊C5 |
| Fitting, socle, derived, Hall | C13×C41 ⋊ C2×C5 |
| Hall | C13×C41⋊C5 ⋊ C2 |
| Hall | D533 ⋊ C5 |
| Hall | C41⋊C5 ⋊ D13 |
| Sylow | C41 ⋊ C5×D13 |
| Sylow | C13 ⋊ D41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C41 | C2×C5 |
| LCS | G ▷ C13×C41 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,13,41|c^a=c^12,d^a=d^40,d^b=d^1092 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5330, 12);