Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C19⋊#64418) |
| unambiguous semidirect product | C19⋊(C3⋊#64418) |
| Fitting, socle | C3×C72×C19 ⋊ D3 |
| derived, Hall | C3×C19×#3862 ⋊ C2 |
| Hall | C72×C19 ⋊ C3⋊D3 |
| Hall | C3×#3862 ⋊ D19 |
| Sylow | C72 ⋊ C3⋊D57 |
| Sylow | C19 ⋊ C3⋊#64418 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C19×#3862 | C2 |
| Fitting, socle | C3×C72×C19 | D3 |
| LCS | G ▷ C3×C19×#3862 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 798 |
Polycyclic presentation:
2,3^2,19,7^2|b^a=b^2,c^a=c^2,d^a=d^18,e^a=e^4f,f^a=e^6f^3,e^b=e^2f^6,f^b=f^4552 conjugacy classes — view the full character table.
| maximal subgroup of | D19×C3⋊#64418, D57×#64418, D3×C19⋊#64418, … |
| maximal normal subgroup of | D19×C3⋊#64418, D57×#64418, D3×C19⋊#64418, … |
| maximal quotient of | C3⋊(C19⋊#10596868), C2×C3⋊(C19⋊#64418) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 392);