Finite Group DatabasebetaFinite Group Databasebeta| order | 5328 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23 |
| direct product | C22×AGL(1,𝔽37) |
| Fitting, socle | C22×C37 ⋊ C4×C9 |
| derived, Sylow | C37 ⋊ C22×C4×C9 |
| Hall | C22×#3866 ⋊ C9 |
| Hall | #66526 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | AGL(1,𝔽37) |
| commutator, hypocenter | C37 | C22×C4×C9 |
| Frattini | C1 | G |
| Fitting, socle | C22×C37 | C4×C9 |
| prime radical | C22×D37⋊C3 | C2×C3 |
| cosocle | D37⋊C3 | C23×C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C22 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 148 |
148 conjugacy classes — view the full character table.
| maximal subgroup of | D4×AGL(1,𝔽37), A4×AGL(1,𝔽37), C2×D3×AGL(1,𝔽37) |
| maximal normal subgroup of | D4×AGL(1,𝔽37), A4×AGL(1,𝔽37) |
| maximal quotient of | D4×AGL(1,𝔽37), C2×D3×AGL(1,𝔽37) |
Past the SmallGroups library coverage — no SmallGroups id.