Finite Group DatabasebetaFinite Group Databasebeta| order | 17748 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊#14520310) |
| Fitting, socle, derived, Hall | C32×C17×C29 ⋊ C4 |
| Hall | C17×C29 ⋊ C3⋊Dic3 |
| Hall | C32×C29 ⋊ Dic17 |
| Hall | C32×C17 ⋊ #1181 |
| Sylow | C29 ⋊ C3⋊Dic51 |
| Sylow | C17 ⋊ C3⋊(C3⋊#1181) |
| Sylow | C32 ⋊ #14520310 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C17×C29 | C4 |
| prime radical, cosocle | C32×C17×D29 | C2 |
| LCS | G ▷ C32×C17×C29 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4437 |
Polycyclic presentation:
2^2,3^2,17,29|a^2=b,c^a=c^2,d^a=d^2,e^a=e^16,f^a=f^17,f^b=f^281227 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17748, 75);