Finite Group DatabasebetaFinite Group Databasebeta| order | 4200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | D3×C7×#1043 |
| Fitting, socle, Hall | C3×C52×C7 ⋊ C2×C4 |
| derived, Hall | C3×C52 ⋊ C2×C4×C7 |
| Hall | C52×C7 ⋊ C4×D3 |
| Sylow | C52 ⋊ C4×D3×C7 |
| Hall | C3×C7 ⋊ C2×#1043 |
| Sylow | C3 ⋊ C2×C7×#1043 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D3×#1043 |
| commutator, hypocenter | C3×C52 | C2×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7 | C2×C4 |
| prime radical | D3×C7×C5⋊D5 | C2 |
| cosocle | C3×C5⋊D5 | C22×C7 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C7 | |
256 conjugacy classes of subgroups.
| transitive degree | μt(G) = 525 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D7×#1043, D3×ΓL(1,𝔽8)×#1043, D3×C7×D5⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | D3×D7×#1043, D3×ΓL(1,𝔽8)×#1043, D3×C7×D5⋊AGL(1,𝔽5), … |
Past the SmallGroups library coverage — no SmallGroups id.