Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C109 · Schur multiplier (H2) = C5 |
| direct product | C109×C3⋊#1039 |
| unambiguous semidirect product | C3⋊(#1039×C109) |
| derived, Hall | C3×C52 ⋊ C4×C109 |
| Hall | C3×C52×C109 ⋊ C4 |
| Hall | C52×C109 ⋊ Dic3 |
| Hall | C3×C109 ⋊ #1039 |
| Sylow | C52 ⋊ Dic3×C109 |
| Sylow | C3 ⋊ #1039×C109 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32700 |
8502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 71);