Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | D147⋊(C5⋊D5) |
| Fitting, derived, Hall | C3×C52×C49 ⋊ C22 |
| Hall | C52×C49 ⋊ C2×D3 |
| Hall | C3×C49 ⋊ C2×C5⋊D5 |
| Hall | C3×C52 ⋊ C2×D49 |
| Sylow | C49 ⋊ D3×C5⋊D5 |
| Sylow | C52 ⋊ D3×D49 |
| Sylow | C3 ⋊ C5⋊D5×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C52×C49 | C22 |
| Frattini | C7 | D21⋊(C5⋊D5) |
| socle | C3×C52×C7 | C2×D7 |
| LCS | G ▷ C3×C52×C49 | |
| UCS | C1 | |
240 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5^2,7^2|f^7=g^6,d^a=d^4,e^a=e^4,f^a=f^6g,g^a=g^6,c^b=c^2,d^b=d^4,e^b=e^4978 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 173);