Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| isoclinism | isoclinic class of AGL(1,𝔽19) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×AGL(1,𝔽19) |
| unambiguous semidirect product | #4296⋊(C2×C25) |
| Fitting, Hall | C19×C25 ⋊ C2×C9 |
| derived, Sylow | C19 ⋊ C2×C9×C25 |
| Hall | C25×#4296 ⋊ C2 |
| Hall | C25×D19 ⋊ C9 |
| Hall | #4296 ⋊ C2×C25 |
| Hall | D19 ⋊ C9×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | AGL(1,𝔽19) |
| commutator, hypocenter | C19 | C2×C9×C25 |
| Frattini | C5 | C5×AGL(1,𝔽19) |
| Fitting | C19×C25 | C2×C9 |
| socle | C5×C19 | C2×C5×C9 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C25 | |
36 conjugacy classes of subgroups.
475 conjugacy classes — view the full character table.
| maximal subgroup of | D25×AGL(1,𝔽19), C2×C25×AGL(1,𝔽19) |
| maximal normal subgroup of | D25×AGL(1,𝔽19), C2×C25×AGL(1,𝔽19) |
| maximal quotient of | C25×#4296⋊C4, C2×C25×AGL(1,𝔽19) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 14);