Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊(C5⋊(#66524⋊C2)) |
| unambiguous semidirect product | #66524⋊(C5⋊D5) |
| derived, Hall | C52×C37 ⋊ C2×C9 |
| Hall | C52×#66524 ⋊ C2 |
| Hall | C5⋊D185 ⋊ C9 |
| Hall | #66524 ⋊ C5⋊D5 |
| Sylow | C37 ⋊ C9×C5⋊D5 |
| Sylow | C52 ⋊ #66524⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊(C5⋊(D37⋊C3)) |
| commutator, hypocenter | C52×C37 | C2×C9 |
| Fitting, socle, cosocle | C3×C52×C37 | C2×C3 |
| prime radical | C3×C5⋊D185 | C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8325 |
Polycyclic presentation:
2,3,5^2,37,3|b^3=f,c^a=c^4,d^a=d^4,e^a=e^36,e^b=e^26576 conjugacy classes — view the full character table.
| maximal subgroup of | #45685945, #45685946, #45685949, … |
| maximal normal subgroup of | #45685945, #45685946, #45685949, … |
| maximal quotient of | #45685808, C2×C5⋊(C5⋊(#66524⋊C2)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 41);