Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D25×#66524 |
| unambiguous semidirect product | C25⋊(C2×#66524) |
| derived, Hall | C25×C37 ⋊ C2×C9 |
| Hall | C25×#66524 ⋊ C2 |
| Hall | C37×D25 ⋊ C9 |
| Sylow | C37 ⋊ C9×D25 |
| Sylow | C25 ⋊ C2×#66524 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D25×C37⋊C3 |
| commutator, hypocenter | C25×C37 | C2×C9 |
| Frattini | C3×C5 | D5×C37⋊C3 |
| Fitting, cosocle | C3×C25×C37 | C2×C3 |
| socle | C3×C5×C37 | C3×D5 |
| prime radical | C3×C37×D25 | C3 |
| LCS | G ▷ C25×C37 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8325 |
630 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45685744, #1035×#66524, D25×#66524⋊C2, … |
| maximal normal subgroup of | #45685744, #1035×#66524, D25×#66524⋊C2, … |
| maximal quotient of | Dic25×#66524, C2×D25×#66524 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 3);