Finite Group DatabasebetaFinite Group Databasebeta| order | 2952 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C3 |
| direct product | C32×#66502 |
| Fitting, socle, Hall | C32×C41 ⋊ C8 |
| derived, Sylow | C41 ⋊ C32×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #66502 |
| commutator, hypocenter | C41 | C32×C8 |
| Frattini | C1 | G |
| Fitting, socle | C32×C41 | C8 |
| prime radical | C32×D41 | C4 |
| cosocle | #4223 | C2×C32 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 369 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#66502, C32×AGL(1,𝔽41), C3×D3×#66502 |
| maximal normal subgroup of | C3⋊D3×#66502, C32×AGL(1,𝔽41), C3×D3×#66502 |
Past the SmallGroups library coverage — no SmallGroups id.