Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| direct product | D37×C52⋊C9 |
| derived, Hall | C52×C37 ⋊ C2×C9 |
| Hall | C37×C52⋊C9 ⋊ C2 |
| Hall | C52×D37 ⋊ C9 |
| Sylow | C37 ⋊ C2×C52⋊C9 |
| Sylow | C52 ⋊ C9×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D37×C52⋊C3 |
| commutator, hypocenter | C52×C37 | C2×C9 |
| Fitting, socle, cosocle | C3×C52×C37 | C2×C3 |
| prime radical | C3×C52×D37 | C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1665 |
660 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45685964, D37×#90646, #45685979, … |
| maximal normal subgroup of | #45685964, D37×#90646, #45685979, … |
| maximal quotient of | Dic37×C52⋊C9, C2×D37×C52⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 50);