Finite Group DatabasebetaFinite Group Databasebeta| order | 5070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D169⋊C3) |
| unambiguous semidirect product | (C169⋊C3)⋊D5 |
| unambiguous semidirect product | D845⋊C3 |
| Fitting, derived, Hall | C5×C169 ⋊ C2×C3 |
| Hall | C5×C169⋊C3 ⋊ C2 |
| Hall | D845 ⋊ C3 |
| Hall | C169⋊C3 ⋊ D5 |
| Sylow | C169 ⋊ C3×D5 |
| Sylow | C5 ⋊ D169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C169 | C2×C3 |
| Frattini | C13 | C5⋊(D13⋊C3) |
| socle | C5×C13 | D13⋊C3 |
| LCS | G ▷ C5×C169 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,13^2|d^13=e^12,c^a=c^4,d^a=d^12e,e^a=e^12,d^b=d^3e^2,e^b=e^3152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5070, 4);