Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic2725⋊C3 |
| derived, Hall | C25×C109 ⋊ C3×C4 |
| Hall | Dic2725 ⋊ C3 |
| Hall | C25×C109⋊C3 ⋊ C4 |
| Hall | C109⋊C3 ⋊ Dic25 |
| Sylow | C109 ⋊ C3×Dic25 |
| Sylow | C25 ⋊ Dic109⋊C3 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10900 |
Polycyclic presentation:
2,3,5,109,2,5|a^2=e,c^5=f^4,c^a=c^4f,d^a=d^108,f^a=f^4,d^b=d^63984 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 12);