Finite Group DatabasebetaFinite Group Databasebeta| order | 5700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | D57⋊(C5⋊D5) |
| Fitting, socle, derived, Hall | C3×C52×C19 ⋊ C22 |
| Hall | C52×C19 ⋊ C2×D3 |
| Hall | C3×C52 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ D3×D19 |
| Sylow | C19 ⋊ D3×C5⋊D5 |
| Sylow | C3 ⋊ D19×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C19 | C22 |
| LCS | G ▷ C3×C52×C19 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5^2,19|d^a=d^4,e^a=e^4,f^a=f^18,c^b=c^2,d^b=d^4,e^b=e^4393 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5700, 139);