Finite Group DatabasebetaFinite Group Databasebeta| order | 6840 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽5)×AGL(1,𝔽19) |
| Fitting, socle, derived, Hall | C5×C19 ⋊ C2×C4×C9 |
| Hall | C5×#4296 ⋊ C2×C4 |
| Hall | AGL(1,𝔽5)×D19 ⋊ C9 |
| Hall | #4296 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C19 ⋊ C2×C9×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×AGL(1,𝔽19) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C19 | C2×C4×C9 |
| prime radical | D5×D19⋊C3 | C2×C3 |
| cosocle | D5×C19⋊C3 | C22×C3 |
| LCS | G ▷ C5×C19 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
95 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×AGL(1,𝔽19) |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×AGL(1,𝔽19) |
| maximal quotient of | C2×AGL(1,𝔽5)×AGL(1,𝔽19) |
| automorphism group of | D95 |
| holomorph of | C5×C19 |
Past the SmallGroups library coverage — no SmallGroups id.