Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D333 |
| unambiguous semidirect product | C9⋊(C52×D37) |
| unambiguous semidirect product | C37⋊(C52×D9) |
| Fitting, Hall | C52×C9×C37 ⋊ C2 |
| derived, Hall | C9×C37 ⋊ C2×C52 |
| Hall | C52×C37 ⋊ D9 |
| Hall | C52×C9 ⋊ D37 |
| Sylow | C37 ⋊ C52×D9 |
| Sylow | C9 ⋊ C52×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D333 |
| commutator, cosocle, hypocenter | C9×C37 | C2×C52 |
| Frattini | C3 | C52×D111 |
| Fitting | C52×C9×C37 | C2 |
| socle | C3×C52×C37 | D3 |
| LCS | G ▷ C9×C37 | |
| UCS | C1 ◁ C52 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8325 |
4200 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D9×D37, C5×D5×D333, C5×D45⋊D37, … |
| maximal normal subgroup of | C52×D9×D37, C5×D5×D333, C5×D45⋊D37, … |
| maximal quotient of | C52×Dic333, C2×C52×D333 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 60);