Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C3 |
| direct product | C25×C3⋊D111 |
| unambiguous semidirect product | C3⋊(C25×D111) |
| unambiguous semidirect product | C37⋊(C3⋊D3×C25) |
| Fitting, Hall | C32×C25×C37 ⋊ C2 |
| derived, Hall | C32×C37 ⋊ C2×C25 |
| Hall | C25×C37 ⋊ C3⋊D3 |
| Hall | C32×C25 ⋊ D37 |
| Sylow | C37 ⋊ C3⋊D3×C25 |
| Sylow | C32 ⋊ C25×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C3⋊D111 |
| commutator, hypocenter | C32×C37 | C2×C25 |
| Frattini | C5 | C5×C3⋊D111 |
| Fitting | C32×C25×C37 | C2 |
| socle, cosocle | C32×C5×C37 | C2×C5 |
| prime radical | C5×C3⋊D111 | C5 |
| LCS | G ▷ C32×C37 | |
| UCS | C1 ◁ C25 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8325 |
4200 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×C25×D37, D25×C3⋊D111, D925⋊(C3⋊D3), … |
| maximal normal subgroup of | C3⋊D3×C25×D37, D25×C3⋊D111, D925⋊(C3⋊D3), … |
| maximal quotient of | C25×C3⋊Dic111, C2×C25×C3⋊D111 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 34);