Finite Group DatabasebetaFinite Group Databasebeta| order | 17748 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#14520308 |
| Fitting, derived, Hall | C9×C17×C29 ⋊ C4 |
| Hall | C17×C29 ⋊ Dic9 |
| Hall | C9×C29 ⋊ #595 |
| Hall | C9×C17 ⋊ #1181 |
| Sylow | C29 ⋊ C9⋊#595 |
| Sylow | C17 ⋊ C9⋊#1181 |
| Sylow | C9 ⋊ #14520308 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C17×C29 | C4 |
| Frattini | C3 | C3⋊#14520308 |
| socle | C3×C17×C29 | Dic3 |
| prime radical | C3×D493 | D3 |
| cosocle | C9×D493 | 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^17,f^a=f^2,d^b=d^16,e^b=e^281119 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17748, 20);