Finite Group DatabasebetaFinite Group Databasebeta| order | 20300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic725⋊C7 |
| derived, Hall | C25×C29 ⋊ C4×C7 |
| Hall | C25×C29⋊C7 ⋊ C4 |
| Hall | Dic725 ⋊ C7 |
| Hall | C29⋊C7 ⋊ Dic25 |
| Sylow | C29 ⋊ C7×Dic25 |
| Sylow | C25 ⋊ Dic29⋊C7 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2900 |
Polycyclic presentation:
2,5,7,29,2,5|a^2=e,b^5=f^4,b^a=b^4f,d^a=d^28,f^a=f^4,d^c=d^16296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20300, 12);