Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | #4296⋊(C7⋊D7) |
| Fitting, socle, derived, Hall | C72×C19 ⋊ C2×C9 |
| Hall | C72×#4296 ⋊ C2 |
| Hall | C7⋊D133 ⋊ C9 |
| Hall | #4296 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ AGL(1,𝔽19) |
| Sylow | C19 ⋊ C9×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C19 | C2×C9 |
| prime radical | (C19⋊C3)⋊(C7⋊D7) | C3 |
| cosocle | C72×C19⋊C3 | C2×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 931 |
Polycyclic presentation:
2,3^2,7^2,19|b^3=c,d^a=d^6,e^a=e^6,f^a=f^18,f^b=f^4,f^c=f^7283 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#4296⋊D7, C7⋊D7×AGL(1,𝔽19), C2×#4296⋊(C7⋊D7) |
| maximal normal subgroup of | D7×#4296⋊D7, C7⋊D7×AGL(1,𝔽19), C2×#4296⋊(C7⋊D7) |
| maximal quotient of | #4296⋊(C7⋊Dic7), C2×#4296⋊(C7⋊D7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 249);