Finite Group DatabasebetaFinite Group Databasebeta| order | 25200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | AGL(1,𝔽7)×#10597182 |
| Fitting, socle, derived | C3×C52×C7 ⋊ C22×C3×C4 |
| Hall | C3×C52×ΓL(1,𝔽8) ⋊ C22×C4 |
| Hall | C52×C7 ⋊ C2×C3×C4×D3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×D5⋊AGL(1,𝔽5) |
| Sylow | C52 ⋊ C4×D3×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C2×C3×#10597182 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C7 | C22×C3×C4 |
| prime radical | AGL(1,𝔽7)×D15⋊D5 | C2 |
| cosocle | C3×C7×C5⋊D5 | C23×C3 |
| LCS | G ▷ C3×C52×C7 | |
| UCS | C1 | |
1120 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 1120 conjugacy classes of subgroups — too many to draw. Only its 125 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.
Past the SmallGroups library coverage — no SmallGroups id.