Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×C23⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C23⋊(C32×C5×AGL(1,𝔽5)) |
| Fitting, socle, Hall | C32×C52×C23 ⋊ C4 |
| derived | C5×C23 ⋊ C32×C4×C5 |
| Hall | C52×C23 ⋊ C32×C4 |
| Hall | C32×C52 ⋊ Dic23 |
| Hall | C32×C23 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ C32×Dic23 |
| Sylow | C23 ⋊ C32×C5×AGL(1,𝔽5) |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4140 |
2205 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 265);