Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C25⋊#64423 |
| Fitting, derived, Hall | C72×C25 ⋊ C2×C3 |
| Hall | C25×#3861 ⋊ C2 |
| Hall | C7×D175 ⋊ C3 |
| Hall | #3861 ⋊ D25 |
| Sylow | C72 ⋊ C3×D25 |
| Sylow | C25 ⋊ #64423 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C72×C25 | C2×C3 |
| Frattini | C5 | C5⋊#64423 |
| socle | C5×C72 | C3×D5 |
| LCS | G ▷ C72×C25 | |
| UCS | C1 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,7^2,5|c^5=f^4,c^a=c^4f,d^a=d^6,f^a=f^4,d^b=d^2,e^b=e^2245 conjugacy classes — view the full character table.
| maximal subgroup of | #64423⋊D25, #64424⋊D25, D25×#64423, … |
| maximal normal subgroup of | #64423⋊D25, #64424⋊D25, D25×#64423, … |
| maximal quotient of | #28412904, C2×C25⋊#64423, C25⋊#11725076, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 55);