Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C5 |
| direct product | C7×#14523574 |
| derived | C52×C7 ⋊ C3×C4×C7 |
| Hall | C7×C7⋊#1039 ⋊ C3 |
| Hall | C7×C7⋊(C52⋊C3) ⋊ C4 |
| Hall | C52×C72 ⋊ C3×C4 |
| Sylow | C72 ⋊ #1039⋊C3 |
| Sylow | C52 ⋊ C7×ΓL(1,𝔽8)⋊C4 |
88 conjugacy classes of subgroups.
490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 346);