Finite Group DatabasebetaFinite Group Databasebeta| order | 4200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#10597182 |
| 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 ⋊ D5⋊AGL(1,𝔽5) |
| Sylow | C3 ⋊ C7×D5⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #10597182 |
| commutator, hypocenter | C3×C52 | C2×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7 | C2×C4 |
| prime radical | C7×D15⋊D5 | C2 |
| cosocle | C3×C5⋊D5 | C22×C7 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C7 | |
152 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 210 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#10597182, D3×C7×D5⋊AGL(1,𝔽5), #72276106, … |
| maximal normal subgroup of | D7×#10597182, D3×C7×D5⋊AGL(1,𝔽5), #72276106, … |
Past the SmallGroups library coverage — no SmallGroups id.