Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | D49⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | (D49⋊(C52⋊C3))⋊C2 |
| unambiguous semidirect product | ((C5⋊D5)⋊(C49⋊C3))⋊C2 |
| unambiguous semidirect product | #20301203⋊C2 |
| Fitting, derived, Hall | C52×C49 ⋊ C22×C3 |
| Hall | C5⋊D5×D49 ⋊ C3 |
| Hall | C52⋊(C49⋊C3) ⋊ C22 |
| Sylow | C49 ⋊ C2×(C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ C2×D49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C49 | C22×C3 |
| Frattini | C7 | D7⋊((C5⋊D5)⋊C3) |
| socle | C52×C7 | C2×AGL(1,𝔽7) |
| LCS | G ▷ C52×C49 | |
| UCS | C1 | |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5^2,7^2|f^7=g^6,f^a=f^6g,g^a=g^6,d^b=d^4,e^b=e^4,d^c=de^3,e^c=d^4e^3,f^c=f^2g^3,g^c=g^2132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 127);