Finite Group DatabasebetaFinite Group Databasebeta| order | 14616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | D3×C3⋊AGL(1,𝔽29) |
| Fitting, socle, derived, Hall | C32×C29 ⋊ C2×C4×C7 |
| Hall | D3×C3⋊#1181 ⋊ C7 |
| Hall | C32×C29⋊C7 ⋊ C2×C4 |
| Hall | C29⋊C7 ⋊ D3×Dic3 |
| Sylow | C29 ⋊ D3×C7×Dic3 |
| Sylow | C32 ⋊ C2×AGL(1,𝔽29) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C29 | C2×C4×C7 |
| prime radical | C3×D3×D29⋊C7 | C2 |
| cosocle | C32×D29 | C22×C7 |
| LCS | G ▷ C32×C29 | |
| UCS | C1 | |
140 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 174 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | D32×AGL(1,𝔽29) |
| maximal normal subgroup of | D32×AGL(1,𝔽29) |
Past the SmallGroups library coverage — no SmallGroups id.