Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#4296⋊D7 |
| unambiguous semidirect product | #4296⋊(C7×D7) |
| Fitting, socle, Hall | C72×C19 ⋊ C2×C9 |
| derived | C7×C19 ⋊ C2×C7×C9 |
| Hall | C72×#4296 ⋊ C2 |
| Hall | C7×D133 ⋊ C9 |
| Hall | #4296 ⋊ C7×D7 |
| Sylow | C72 ⋊ AGL(1,𝔽19) |
| Sylow | C19 ⋊ C7×C9×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #4296⋊D7 |
| commutator, hypocenter | C7×C19 | C2×C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C72×C19 | C2×C9 |
| prime radical | C7×(C19⋊C3)⋊D7 | C3 |
| cosocle | C7×C19⋊C3 | C2×C3×C7 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C7 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 266 |
364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D7×AGL(1,𝔽19), D7×#4296⋊D7, (#4296⋊D7)⋊D7, … |
| maximal normal subgroup of | C7×D7×AGL(1,𝔽19), D7×#4296⋊D7, (#4296⋊D7)⋊D7, … |
| maximal quotient of | C7×#4296⋊Dic7, C2×C7×#4296⋊D7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 172);