Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct 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 |
78 conjugacy classes of subgroups.
890 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 88);