Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C49⋊#1043) |
| unambiguous semidirect product | C49⋊(C3⋊#1043) |
| Fitting, derived, Hall | C3×C52×C49 ⋊ C4 |
| Hall | C52×C49 ⋊ Dic3 |
| Hall | C3×C49 ⋊ #1043 |
| Hall | C3×C52 ⋊ Dic49 |
| Sylow | C49 ⋊ C3⋊#1043 |
| Sylow | C52 ⋊ Dic147 |
| Sylow | C3 ⋊ C49⋊#1043 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C52×C49 | C4 |
| Frattini | C7 | C3⋊(C7⋊#1043) |
| socle | C3×C52×C7 | Dic7 |
| prime radical | C3×C7×C5⋊D5 | D7 |
| cosocle | C3×C49×C5⋊D5 | C2 |
| LCS | G ▷ C3×C52×C49 | |
| UCS | C1 | |
144 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5^2,7^2|a^2=b,f^7=g^6,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^6g,g^a=g^6,d^b=d^4,e^b=e^41032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 164);