Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊(C5⋊#64418) |
| Fitting, socle, Hall | C52×C72 ⋊ D3 |
| derived, Hall | C52×#3862 ⋊ C2 |
| Hall | #3862 ⋊ C5⋊D5 |
| Sylow | C72 ⋊ C3⋊(C5⋊D5) |
| Sylow | C52 ⋊ #64418 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C52×#3862 | C2 |
| Fitting, socle | C52×C72 | D3 |
| LCS | G ▷ C52×#3862 | |
| UCS | C1 | |
112 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=f,f^a=e,e^b=e^4,f^b=f^2248 conjugacy classes — view the full character table.
| maximal subgroup of | #64418⋊(C5⋊D5), #28413305, C5⋊D5×#64418, … |
| maximal normal subgroup of | #64418⋊(C5⋊D5), #28413305, C5⋊D5×#64418, … |
| maximal quotient of | #28413161, C2×C5⋊(C5⋊#64418), C5⋊(C5⋊#11725071), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 105);