Finite Group DatabasebetaFinite Group Databasebeta| order | 16800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | AGL(1,𝔽5)2×AGL(1,𝔽7) |
| Fitting, socle, derived, Hall | C52×C7 ⋊ C2×C3×C42 |
| Hall | D7×AGL(1,𝔽5)2 ⋊ C3 |
| Hall | C52×ΓL(1,𝔽8) ⋊ C2×C42 |
| Sylow | C52 ⋊ C42×AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ C2×AGL(1,𝔽5)2 |
| Sylow | C7 ⋊ C2×C3×AGL(1,𝔽5)2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C7 | C2×C3×C42 |
| prime radical | D52×AGL(1,𝔽7) | C22 |
| cosocle | C7×D52 | C23×C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 | |
896 conjugacy classes of subgroups.
| transitive degree | μt(G) = 140 |
175 conjugacy classes — view the full character table.
| holomorph of | C7×AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.