Finite Group DatabasebetaFinite Group Databasebeta| order | 16206 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C73⋊C3)⋊D37 |
| Fitting, socle, derived, Hall | C37×C73 ⋊ C2×C3 |
| Hall | C37×C73⋊C3 ⋊ C2 |
| Hall | D2701 ⋊ C3 |
| Hall | C73⋊C3 ⋊ D37 |
| Sylow | C73 ⋊ C3×D37 |
| Sylow | C37 ⋊ D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C73 | C2×C3 |
| LCS | G ▷ C37×C73 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2701 |
Polycyclic presentation:
2,3,37,73|c^a=c^36,d^a=d^72,d^b=d^8504 conjugacy classes — view the full character table.
| maximal subgroup of | #44569442, #44569443, D37×D73⋊C3, … |
| maximal normal subgroup of | #44569442, #44569443, D37×D73⋊C3, … |
| maximal quotient of | #44569418, C2×(C73⋊C3)⋊D37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16206, 21);