Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#19150288 |
| Fitting, socle, derived | C3×C72×C19 ⋊ C2×C3 |
| Hall | C3×C19×#3861 ⋊ C2 |
| Hall | C72×C19 ⋊ C3×D3 |
| Hall | C3×#3861 ⋊ D19 |
| Sylow | C72 ⋊ C3×D57 |
| Sylow | C19 ⋊ C3⋊#64424 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C19 | C2×C3 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 | |
180 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2793 |
Polycyclic presentation:
2,3^2,7^2,19|c^a=c^2,d^a=d^6,e^a=e^6,f^a=f^18,d^b=d^2,e^b=e^2546 conjugacy classes — view the full character table.
| maximal subgroup of | D19×C3⋊#64424, D57×#64424, D3×#19150288, … |
| maximal normal subgroup of | D19×C3⋊#64424, D57×#64424, D3×#19150288, … |
| maximal quotient of | C3⋊#26013821, C2×C3⋊#19150288 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 350);