Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊D1197 |
| unambiguous semidirect product | C9⋊(C7⋊D133) |
| unambiguous semidirect product | C19⋊(C7⋊D63) |
| Fitting, derived, Hall | C72×C9×C19 ⋊ C2 |
| Hall | C72×C19 ⋊ D9 |
| Hall | C72×C9 ⋊ D19 |
| Hall | C9×C19 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D171 |
| Sylow | C19 ⋊ C7⋊D63 |
| Sylow | C9 ⋊ C7⋊D133 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C72×C9×C19 | C2 |
| Frattini | C3 | C3⋊(C7⋊D133) |
| socle | C3×C72×C19 | D3 |
| LCS | G ▷ C72×C9×C19 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8379 |
Polycyclic presentation:
2,3,7^2,19,3|b^3=f^2,b^a=b^2f,c^a=c^6,d^a=d^6,e^a=e^18,f^a=f^24191 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×C7⋊D63, C7⋊D7×D171, D9×C7⋊D133, … |
| maximal normal subgroup of | D19×C7⋊D63, C7⋊D7×D171, D9×C7⋊D133, … |
| maximal quotient of | C7⋊Dic1197, C2×C7⋊D1197 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 160);