Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D49×#3874 |
| Fitting, Hall | C52×C49 ⋊ C2×D3 |
| derived, Hall | C49×C52⋊C3 ⋊ C22 |
| Hall | C52⋊C3 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×#3874 |
| Sylow | C52 ⋊ D3×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C49×C52⋊C3 | C22 |
| Frattini | C7 | D7×#3874 |
| Fitting | C52×C49 | C2×D3 |
| socle | C52×C7 | D3×D7 |
| LCS | G ▷ C49×C52⋊C3 | |
| UCS | C1 | |
90 conjugacy classes of subgroups.
338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 120);