Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C25⋊(D49⋊C3) |
| unambiguous semidirect product | (C49⋊C3)⋊D25 |
| unambiguous semidirect product | D1225⋊C3 |
| Fitting, derived, Hall | C25×C49 ⋊ C2×C3 |
| Hall | C25×C49⋊C3 ⋊ C2 |
| Hall | D1225 ⋊ C3 |
| Hall | C49⋊C3 ⋊ D25 |
| Sylow | C49 ⋊ C3×D25 |
| Sylow | C25 ⋊ D49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C49 | C2×C3 |
| Frattini, socle | C5×C7 | C5⋊AGL(1,𝔽7) |
| LCS | G ▷ C25×C49 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,7,5,7|c^5=e^4,d^7=f^6,c^a=c^4e,d^a=d^6f,e^a=e^4,f^a=f^6,d^b=d^2f^3,f^b=f^2242 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 4);