Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C1 |
| direct product | C3×C37×D75 |
| unambiguous semidirect product | C3⋊(C3×C37×D25) |
| unambiguous semidirect product | C25⋊(C3×D3×C37) |
| Fitting, Hall | C32×C25×C37 ⋊ C2 |
| derived | C3×C25 ⋊ C2×C3×C37 |
| Hall | C25×C37 ⋊ C3×D3 |
| Hall | C32×C37 ⋊ D25 |
| Hall | C32×C25 ⋊ C2×C37 |
| Sylow | C25 ⋊ C3×D3×C37 |
| Sylow | C32 ⋊ C37×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C37 | D75 |
| commutator, cosocle, hypocenter | C3×C25 | C2×C3×C37 |
| Frattini | C5 | C3×D15×C37 |
| Fitting | C32×C25×C37 | C2 |
| socle | C32×C5×C37 | D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C3×C37 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5550 |
4329 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D37×D75, C3×D3×C37×D25, C3×D75⋊D37, … |
| maximal normal subgroup of | C3×D37×D75, C3×D3×C37×D25, C3×D75⋊D37, … |
| maximal quotient of | C3×C37×Dic75, C2×C3×C37×D75 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 31);