Finite Group DatabasebetaFinite Group Databasebeta| order | 16800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D3×D7×D5⋊AGL(1,𝔽5) |
| Fitting, socle, derived, Hall | C3×C52×C7 ⋊ C23×C4 |
| Hall | C52×C7 ⋊ C22×C4×D3 |
| Hall | C3×C52 ⋊ C22×C4×D7 |
| Sylow | C52 ⋊ C2×C4×D3×D7 |
| Hall | C3×C7 ⋊ C22×D5⋊AGL(1,𝔽5) |
| Sylow | C7 ⋊ C2×D3×D5⋊AGL(1,𝔽5) |
| Sylow | C3 ⋊ C2×D7×D5⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C7 | C23×C4 |
| prime radical | D3×D52×D7 | C2 |
| cosocle | C3×C7×C5⋊D5 | C24 |
| LCS | G ▷ C3×C52×C7 | |
| UCS | C1 | |
2104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 210 |
210 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.