Finite Group DatabasebetaFinite Group Databasebeta| order | 8400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×D5⋊(C7⋊AGL(1,𝔽5)) |
| Fitting, socle, derived, Hall | C3×C52×C7 ⋊ C22×C4 |
| Hall | C52×C7 ⋊ C2×C4×D3 |
| Hall | C3×C52 ⋊ C22×Dic7 |
| Sylow | C52 ⋊ C2×D3×Dic7 |
| Hall | C3×C7 ⋊ C2×D5⋊AGL(1,𝔽5) |
| Sylow | C7 ⋊ D3×D5⋊AGL(1,𝔽5) |
| Sylow | C3 ⋊ C2×D5⋊(C7⋊AGL(1,𝔽5)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C7 | C22×C4 |
| prime radical | D3×C7×D52 | C2 |
| cosocle | C3×C7×C5⋊D5 | C23 |
| LCS | G ▷ C3×C52×C7 | |
| UCS | C1 | |
496 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 210 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D7×D5⋊AGL(1,𝔽5) |
| maximal normal subgroup of | D3×D7×D5⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.