Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5×C7 |
| unambiguous semidirect product | C3⋊(C5⋊(C5⋊(C7⋊D7))) |
| unambiguous semidirect product | C5⋊(C3⋊(C5⋊(C7⋊D7))) |
| unambiguous semidirect product | C7⋊(C3⋊(C5⋊D35)) |
| Fitting, socle, derived, Hall | C3×C52×C72 ⋊ C2 |
| Hall | C52×C72 ⋊ D3 |
| Hall | C3×C72 ⋊ C5⋊D5 |
| Hall | C3×C52 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C3⋊(C5⋊D5) |
| Sylow | C52 ⋊ C3⋊(C7⋊D7) |
| Sylow | C3 ⋊ C5⋊(C5⋊(C7⋊D7)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C72 | C2 |
| LCS | G ▷ C3×C52×C72 | |
| UCS | C1 | |
320 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,7^2|b^a=b^2,c^a=c^4,d^a=d^4,e^a=e^6,f^a=f^61839 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 155);