Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| isoclinism | isoclinic class of AGL(1,𝔽19) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72×C9 · Schur multiplier (H2) = C7 |
| direct product | C72×AGL(1,𝔽19) |
| unambiguous semidirect product | #4296⋊(C2×C72) |
| Fitting, socle, Hall | C72×C19 ⋊ C2×C9 |
| derived, Sylow | C19 ⋊ C2×C72×C9 |
| Hall | C72×#4296 ⋊ C2 |
| Hall | C72×D19 ⋊ C9 |
| Hall | #4296 ⋊ C2×C72 |
| Hall | D19 ⋊ C72×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | AGL(1,𝔽19) |
| commutator, hypocenter | C19 | C2×C72×C9 |
| Frattini | C1 | G |
| Fitting, socle | C72×C19 | C2×C9 |
| prime radical | C72×D19⋊C3 | C3 |
| cosocle | C19⋊C3 | C2×C3×C72 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C72 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 931 |
931 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 162);