Finite Group DatabasebetaFinite Group Databasebeta| order | 9744 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C22×C3⋊AGL(1,𝔽29) |
| Fitting, socle | C22×C3×C29 ⋊ C4×C7 |
| derived, Hall | C3×C29 ⋊ C22×C4×C7 |
| Hall | C22×C3⋊#1181 ⋊ C7 |
| Hall | C3×C29⋊C7 ⋊ C22×C4 |
| Hall | C29⋊C7 ⋊ C22×Dic3 |
| Sylow | C29 ⋊ C22×C7×Dic3 |
| Sylow | C3 ⋊ C22×AGL(1,𝔽29) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊AGL(1,𝔽29) |
| commutator, hypocenter | C3×C29 | C22×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C29 | C4×C7 |
| prime radical | C22×C3×D29⋊C7 | C2 |
| cosocle | C3×D29 | C23×C7 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C22 | |
216 conjugacy classes of subgroups.
180 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D3×AGL(1,𝔽29), C2×C4×C3⋊AGL(1,𝔽29), C2×Dic3×AGL(1,𝔽29) |
| maximal normal subgroup of | C22×D3×AGL(1,𝔽29), C2×C4×C3⋊AGL(1,𝔽29), C2×Dic3×AGL(1,𝔽29) |
| maximal quotient of | C2×C4×C3⋊AGL(1,𝔽29) |
Past the SmallGroups library coverage — no SmallGroups id.