Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C41 · Schur multiplier (H2) = C3 |
| direct product | C5×C41×C3⋊ΓL(1,𝔽16) |
| unambiguous semidirect product | C3⋊(C5×C41×ΓL(1,𝔽16)) |
| Fitting, socle, Hall | C32×C52×C41 ⋊ C4 |
| derived | C32×C5 ⋊ C4×C5×C41 |
| Hall | C52×C41 ⋊ C3⋊Dic3 |
| Hall | C32×C41 ⋊ C5×AGL(1,𝔽5) |
| Hall | C32×C52 ⋊ C4×C41 |
| Sylow | C52 ⋊ C3⋊Dic3×C41 |
| Sylow | C32 ⋊ C5×AGL(1,𝔽5)×C41 |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7380 |
4305 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 574);