Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C109 · Schur multiplier (H2) = C1 |
| direct product | C109×C3⋊#1035 |
| unambiguous semidirect product | C3⋊(#1035×C109) |
| Fitting, Hall | C3×C25×C109 ⋊ C4 |
| derived, Hall | C3×C25 ⋊ C4×C109 |
| Hall | C25×C109 ⋊ Dic3 |
| Hall | C3×C109 ⋊ #1035 |
| Sylow | C25 ⋊ Dic3×C109 |
| Sylow | C3 ⋊ #1035×C109 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8175 |
2616 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 33);