Finite Group DatabasebetaFinite Group Databasebeta| order | 7866 |
| isoclinism | isoclinic class of AGL(1,𝔽19) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×AGL(1,𝔽19) |
| unambiguous semidirect product | #4296⋊(C2×C23) |
| Fitting, socle, Hall | C19×C23 ⋊ C2×C9 |
| derived, Sylow | C19 ⋊ C2×C9×C23 |
| Hall | C23×#4296 ⋊ C2 |
| Hall | C23×D19 ⋊ C9 |
| Hall | #4296 ⋊ C2×C23 |
| Hall | D19 ⋊ C9×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | AGL(1,𝔽19) |
| commutator, hypocenter | C19 | C2×C9×C23 |
| Frattini | C1 | G |
| Fitting, socle | C19×C23 | C2×C9 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
437 conjugacy classes — view the full character table.
| maximal subgroup of | D23×AGL(1,𝔽19), C2×C23×AGL(1,𝔽19) |
| maximal normal subgroup of | D23×AGL(1,𝔽19), C2×C23×AGL(1,𝔽19) |
| maximal quotient of | C23×#4296⋊C4, C2×C23×AGL(1,𝔽19) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7866, 14);