Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5×C7 |
| unambiguous semidirect product | C3⋊#19096693 |
| Fitting, socle, derived, Hall | C3×C52×C72 ⋊ C4 |
| Hall | C52×C72 ⋊ Dic3 |
| Hall | C3×C72 ⋊ #1039 |
| Hall | C3×C52 ⋊ #5997 |
| Sylow | C72 ⋊ C3⋊#1039 |
| Sylow | C52 ⋊ C3⋊#5997 |
| Sylow | C3 ⋊ #19096693 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C72 | C4 |
| prime radical, cosocle | C3×C52×C7⋊D7 | C2 |
| LCS | G ▷ C3×C52×C72 | |
| UCS | C1 | |
224 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5^2,7^2|a^2=b,c^a=c^2,d^a=d^4,e^a=e^4,f^a=f^4g^6,g^a=f^3g^3,f^b=f^6,g^b=g^6978 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 710);