Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D1665 |
| unambiguous semidirect product | C9⋊(C5⋊D185) |
| unambiguous semidirect product | C37⋊(C5⋊D45) |
| Fitting, derived, Hall | C52×C9×C37 ⋊ C2 |
| Hall | C52×C37 ⋊ D9 |
| Hall | C9×C37 ⋊ C5⋊D5 |
| Hall | C52×C9 ⋊ D37 |
| Sylow | C37 ⋊ C5⋊D45 |
| Sylow | C52 ⋊ D333 |
| Sylow | C9 ⋊ C5⋊D185 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C9×C37 | C2 |
| Frattini | C3 | C3⋊(C5⋊D185) |
| socle | C3×C52×C37 | D3 |
| LCS | G ▷ C52×C9×C37 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8325 |
Polycyclic presentation:
2,3,5^2,37,3|b^3=f^2,b^a=b^2f,c^a=c^4,d^a=d^4,e^a=e^36,f^a=f^24164 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D37×C5⋊D45, C5⋊D5×D333, D9×C5⋊D185, … |
| maximal normal subgroup of | D37×C5⋊D45, C5⋊D5×D333, D9×C5⋊D185, … |
| maximal quotient of | C9⋊#16814867, C2×C5⋊D1665 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 64);