Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C7 |
| direct product | C5×C3⋊#11758267 |
| unambiguous semidirect product | C3⋊(C5×#11758267) |
| Fitting, socle, Hall | C3×C52×C72 ⋊ C4 |
| derived | C3×C5×C72 ⋊ C4×C5 |
| Hall | C52×C72 ⋊ Dic3 |
| Hall | C3×C72 ⋊ C5×Dic5 |
| Hall | C3×C52 ⋊ #5997 |
| Sylow | C72 ⋊ C5×Dic15 |
| Sylow | C52 ⋊ C3⋊#5997 |
| Sylow | C3 ⋊ C5×#11758267 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊#11758267 |
| commutator, hypocenter | C3×C5×C72 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C4 |
| prime radical | C3×C52×C7⋊D7 | C2 |
| cosocle | C3×C5×C7⋊D7 | C2×C5 |
| LCS | G ▷ C3×C5×C72 | |
| UCS | C1 ◁ C5 | |
192 conjugacy classes of subgroups.
990 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 683);