Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×ΓL(1,𝔽8)⋊Dic7 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C52×Dic7) |
| derived, Sylow | C72 ⋊ C3×C4×C52 |
| Hall | C52×C7⋊Dic7 ⋊ C3 |
| Hall | C52×C7×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C52×C72 ⋊ C3×C4 |
| Hall | C7⋊Dic7 ⋊ C3×C52 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C4×C52 |
240 conjugacy classes of subgroups.
1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 316);