Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C5 |
| direct product | C7×C7⋊#64480 |
| unambiguous semidirect product | C7⋊(C7×#64480) |
| Fitting, socle, Hall | C52×C72 ⋊ Dic3 |
| derived | C7×C52⋊C3 ⋊ C4×C7 |
| Hall | C72×C52⋊C3 ⋊ C4 |
| Hall | C52⋊C3 ⋊ C7×Dic7 |
| Sylow | C72 ⋊ #64480 |
| Sylow | C52 ⋊ C7×Dic21 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C7⋊#64480 |
| commutator, hypocenter | C7×C52⋊C3 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C72 | Dic3 |
| prime radical | C72×(C5⋊D5)⋊C3 | C2 |
| cosocle | C7×(C5⋊D5)⋊C3 | C2×C7 |
| LCS | G ▷ C7×C52⋊C3 | |
| UCS | C1 ◁ C7 | |
108 conjugacy classes of subgroups.
266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 548);