Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C37⋊#90646 |
| derived, Hall | C37×C52⋊C9 ⋊ C2 |
| Hall | C52×C37 ⋊ D9 |
| Hall | C52⋊C9 ⋊ D37 |
| Sylow | C37 ⋊ #90646 |
| Sylow | C52 ⋊ D333 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C37×C52⋊C9 | C2 |
| Frattini | C3 | C37⋊#3874 |
| Fitting, socle | C3×C52×C37 | D3 |
| LCS | G ▷ C37×C52⋊C9 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1665 |
Polycyclic presentation:
2,3,37,5^2,3|b^3=f^2,b^a=b^2f,c^a=c^36,d^a=d^2e,e^a=d^2e^3,f^a=f^2,d^b=d^2e^4,e^b=d^2e^2618 conjugacy classes — view the full character table.
| maximal subgroup of | #90646⋊D37, ((C5⋊D5)⋊C9)⋊D37, D37×#90646, … |
| maximal normal subgroup of | #90646⋊D37, ((C5⋊D5)⋊C9)⋊D37, D37×#90646, … |
| maximal quotient of | #45685811, C2×C37⋊#90646 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 44);