Finite Group DatabasebetaFinite Group Databasebeta| order | 5160 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽5)×D43⋊C3 |
| Fitting, socle, derived, Hall | C5×C43 ⋊ C2×C3×C4 |
| Hall | AGL(1,𝔽5)×D43 ⋊ C3 |
| Hall | C5×C43⋊C3 ⋊ C2×C4 |
| Hall | C43⋊C3 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C43 ⋊ C2×C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×D43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C43 | C2×C3×C4 |
| prime radical | D5×D43⋊C3 | C2 |
| cosocle | D5×C43 | C22×C3 |
| LCS | G ▷ C5×C43 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 215 |
65 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×AGL(1,𝔽43) |
| maximal normal subgroup of | AGL(1,𝔽5)×AGL(1,𝔽43) |
Past the SmallGroups library coverage — no SmallGroups id.