Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊(C5⋊(D49⋊C3)) |
| unambiguous semidirect product | (C49⋊C3)⋊(C5⋊D5) |
| Fitting, derived, Hall | C52×C49 ⋊ C2×C3 |
| Hall | C52×C49⋊C3 ⋊ C2 |
| Hall | C5⋊D245 ⋊ C3 |
| Hall | C49⋊C3 ⋊ C5⋊D5 |
| Sylow | C49 ⋊ C3×C5⋊D5 |
| Sylow | C52 ⋊ D49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C52×C49 | C2×C3 |
| Frattini | C7 | C5⋊(C5⋊AGL(1,𝔽7)) |
| socle | C52×C7 | AGL(1,𝔽7) |
| LCS | G ▷ C52×C49 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,7^2|e^7=f^6,c^a=c^4,d^a=d^4,e^a=e^6f,f^a=f^6,e^b=e^4f^5,f^b=f^4242 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 20);