Finite Group DatabasebetaFinite Group Databasebeta| order | 34104 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽7)×AGL(1,𝔽29) |
| Fitting, socle, derived | C7×C29 ⋊ C2×C3×C4×C7 |
| Hall | D7×AGL(1,𝔽29) ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C29⋊C7 ⋊ C2×C4 |
| Hall | C7×C29⋊C7 ⋊ C2×C3×C4 |
| Sylow | C29 ⋊ C4×C7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C29 | C2×C3×C4×C7 |
| prime radical | AGL(1,𝔽7)×D29⋊C7 | C2 |
| cosocle | C7×D29 | C22×C3×C7 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 | |
134 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 203 |
203 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.