Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×C5⋊(#66526⋊C2) |
| unambiguous semidirect product | C5⋊(C5×#66526⋊C2) |
| unambiguous semidirect product | #66526⋊(C5×D5) |
| Fitting, socle, Hall | C52×C37 ⋊ C2×C9 |
| derived | C5×C37 ⋊ C2×C5×C9 |
| Hall | C52×#66526 ⋊ C2 |
| Hall | C5×D185 ⋊ C9 |
| Hall | #66526 ⋊ C5×D5 |
| Sylow | C37 ⋊ C5×C9×D5 |
| Sylow | C52 ⋊ #66526⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C5⋊(#66526⋊C2) |
| commutator, hypocenter | C5×C37 | C2×C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C52×C37 | C2×C9 |
| prime radical | C5×C5⋊(D37⋊C3) | C3 |
| cosocle | C5×C37⋊C3 | C2×C3×C5 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 370 |
230 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D5×#66526⋊C2, C5×#20269082, C5×#20269083, … |
| maximal normal subgroup of | C5×D5×#66526⋊C2, C5×#20269082, C5×#20269083, … |
| maximal quotient of | C5×#20269058, C2×C5×C5⋊(#66526⋊C2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 67);