Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C49⋊#64480 |
| Fitting, Hall | C52×C49 ⋊ Dic3 |
| derived, Hall | C49×C52⋊C3 ⋊ C4 |
| Hall | C52⋊C3 ⋊ Dic49 |
| Sylow | C49 ⋊ #64480 |
| Sylow | C52 ⋊ Dic147 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C49×C52⋊C3 | C4 |
| Frattini | C7 | C7⋊#64480 |
| Fitting | C52×C49 | Dic3 |
| socle | C52×C7 | Dic21 |
| prime radical | C7×(C5⋊D5)⋊C3 | D7 |
| cosocle | C49×(C5⋊D5)⋊C3 | C2 |
| LCS | G ▷ C49×C52⋊C3 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7,5^2,7|a^2=b,d^7=g^6,c^a=c^2,d^a=d^6g,e^a=e^3,f^a=ef^2,g^a=g^6,e^b=e^4,f^b=f^4,e^c=ef,f^c=e^2f^3248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 126);