Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#11725071 |
| derived, Hall | C19×#89205 ⋊ C2 |
| Hall | C72×C19 ⋊ D9 |
| Hall | #89205 ⋊ D19 |
| Sylow | C72 ⋊ D171 |
| Sylow | C19 ⋊ #11725071 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C19×#89205 | C2 |
| Frattini | C3 | C19⋊#64418 |
| Fitting, socle | C3×C72×C19 | D3 |
| LCS | G ▷ C19×#89205 | |
| UCS | C1 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1197 |
Polycyclic presentation:
2,3,19,7^2,3|b^3=f^2,b^a=b^2f,c^a=c^18,d^a=d^2e^3,e^a=d^6e^5,f^a=f^2,d^b=d^4e^4,e^b=e^2552 conjugacy classes — view the full character table.
| maximal subgroup of | #11725071⋊D19, #45691594, D19×#11725071, … |
| maximal normal subgroup of | #11725071⋊D19, #45691594, D19×#11725071, … |
| maximal quotient of | C19⋊#13183527, C2×C19⋊#11725071 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 140);