Finite Group DatabasebetaFinite Group Databasebeta| order | 17748 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#14520309 |
| Fitting, derived, Hall | C9×C17×C29 ⋊ C4 |
| Hall | C17×C29 ⋊ Dic9 |
| Hall | C9×C29 ⋊ #595 |
| Hall | C9×C17 ⋊ Dic29 |
| Sylow | C29 ⋊ C9⋊#595 |
| Sylow | C17 ⋊ Dic261 |
| Sylow | C9 ⋊ #14520309 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C17×C29 | C4 |
| Frattini | C3 | C3⋊#14520309 |
| socle | C3×C17×C29 | Dic3 |
| prime radical | C3×C29×D17 | D3 |
| cosocle | C9×C29×D17 | C2 |
| LCS | G ▷ C9×C17×C29 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4437 |
Polycyclic presentation:
2^2,3,17,29,3|a^2=b,c^3=f^2,c^a=c^2f,d^a=d^13,e^a=e^28,f^a=f^2,d^b=d^161308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17748, 22);