Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊Dic175 |
| derived, Hall | C72×C25 ⋊ C3×C4 |
| Hall | C7⋊Dic175 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8)×C25 ⋊ C4 |
| Hall | C7×ΓL(1,𝔽8) ⋊ Dic25 |
| Sylow | C72 ⋊ C3×Dic25 |
| Sylow | C25 ⋊ ΓL(1,𝔽8)⋊Dic7 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,7^2,2,5|a^2=f,c^5=g^4,c^a=c^4g,d^a=d^6,e^a=e^6,g^a=g^4,d^b=d^2884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 85);