Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C25⋊(#66524⋊C2) |
| unambiguous semidirect product | #66524⋊D25 |
| derived, Hall | C25×C37 ⋊ C2×C9 |
| Hall | C25×#66524 ⋊ C2 |
| Hall | D925 ⋊ C9 |
| Hall | #66524 ⋊ D25 |
| Sylow | C37 ⋊ C9×D25 |
| Sylow | C25 ⋊ #66524⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C25⋊(D37⋊C3) |
| commutator, hypocenter | C25×C37 | C2×C9 |
| Frattini | C3×C5 | C5⋊(D37⋊C3) |
| Fitting, cosocle | C3×C25×C37 | C2×C3 |
| socle | C3×C5×C37 | C3×D5 |
| prime radical | C3×D925 | C3 |
| LCS | G ▷ C25×C37 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8325 |
Polycyclic presentation:
2,3,5,37,3,5|b^3=e,c^5=f^4,c^a=c^4f,d^a=d^36,f^a=f^4,d^b=d^10576 conjugacy classes — view the full character table.
| maximal subgroup of | #45685742, #45685743, D25×#66524⋊C2, … |
| maximal normal subgroup of | #45685742, #45685743, D25×#66524⋊C2, … |
| maximal quotient of | #45685731, C2×C25⋊(#66524⋊C2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 4);