Finite Group DatabasebetaFinite Group Databasebeta| order | 18624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | D3×#15690911 |
| Fitting, socle, derived, Hall | C3×C97 ⋊ C2×C32 |
| Sylow | C97 ⋊ D3×C32 |
| Sylow | C3 ⋊ C2×#15690911 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C97 | C2×C32 |
| prime radical | D3×D97 | C16 |
| cosocle | C3×#13095525 | C22 |
| LCS | G ▷ C3×C97 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
105 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽97) |
| maximal normal subgroup of | D3×AGL(1,𝔽97) |
Past the SmallGroups library coverage — no SmallGroups id.