Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)⋊D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊Dic25 |
| unambiguous semidirect product | Dic175⋊C3 |
| derived, Hall | C7×C25 ⋊ C3×C4 |
| Hall | Dic175 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C25 ⋊ C4 |
| Sylow | C25 ⋊ ΓL(1,𝔽8)⋊C4 |
| Hall | ΓL(1,𝔽8) ⋊ Dic25 |
| Sylow | C7 ⋊ C3×Dic25 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 700 |
Polycyclic presentation:
2,3,5,7,2,5|a^2=e,c^5=f^4,c^a=c^4f,d^a=d^6,f^a=f^4,d^b=d^2134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 4);