Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| isoclinism | isoclinic class of C3⋊D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C3 |
| direct product | C37×C3⋊D75 |
| unambiguous semidirect product | C3⋊(C37×D75) |
| unambiguous semidirect product | C25⋊(C3⋊D3×C37) |
| Fitting, Hall | C32×C25×C37 ⋊ C2 |
| derived, Hall | C32×C25 ⋊ C2×C37 |
| Hall | C25×C37 ⋊ C3⋊D3 |
| Hall | C32×C37 ⋊ D25 |
| Sylow | C25 ⋊ C3⋊D3×C37 |
| Sylow | C32 ⋊ C37×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C3⋊D75 |
| commutator, cosocle, hypocenter | C32×C25 | C2×C37 |
| Frattini | C5 | C37×C3⋊D15 |
| Fitting | C32×C25×C37 | C2 |
| socle | C32×C5×C37 | D5 |
| LCS | G ▷ C32×C25 | |
| UCS | C1 ◁ C37 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8325 |
4218 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D37×C3⋊D75, C3⋊D3×C37×D25, D925⋊(C3⋊D3), … |
| maximal normal subgroup of | D37×C3⋊D75, C3⋊D3×C37×D25, D925⋊(C3⋊D3), … |
| maximal quotient of | C37×C3⋊Dic75, C2×C37×C3⋊D75 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 35);