Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C37⋊C3×D75 |
| unambiguous semidirect product | C3⋊(D25×C37⋊C3) |
| unambiguous semidirect product | C25⋊(D3×C37⋊C3) |
| unambiguous semidirect product | (C37×D75)⋊C3 |
| Fitting, derived | C3×C25×C37 ⋊ C2×C3 |
| Hall | C3×C25×C37⋊C3 ⋊ C2 |
| Hall | C25×C37 ⋊ C3×D3 |
| Hall | C3×C37⋊C3 ⋊ D25 |
| Sylow | C37 ⋊ C3×D75 |
| Sylow | C25 ⋊ D3×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C25×C37 | C2×C3 |
| Frattini | C5 | D15×C37⋊C3 |
| socle | C3×C5×C37 | C3×D5 |
| LCS | G ▷ C3×C25×C37 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2775 |
585 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D75×D37⋊C3, D75⋊(D37⋊C3), D3×D25×C37⋊C3, … |
| maximal normal subgroup of | D75×D37⋊C3, D75⋊(D37⋊C3), D3×D25×C37⋊C3, … |
| maximal quotient of | C37⋊C3×Dic75, C2×C37⋊C3×D75 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 24);