Finite Group DatabasebetaFinite Group Databasebeta| order | 17748 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C17×C29 ⋊ C4 |
| Hall | C17×C29 ⋊ #157 |
| Hall | C32×C29 ⋊ Dic17 |
| Hall | C32×C17 ⋊ #1181 |
| Sylow | C29 ⋊ #10597480 |
| Sylow | C17 ⋊ #11760329 |
| Sylow | C32 ⋊ #14520310 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C17×C29 | C4 |
| prime radical, cosocle | C17×C3⋊D87 | C2 |
| LCS | G ▷ C32×C17×C29 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2958 |
Polycyclic presentation:
2^2,3^2,17,29|a^2=b,c^a=cd,d^a=cd^2,e^a=e^16,f^a=f^17,c^b=c^2,d^b=d^2,f^b=f^281125 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17748, 99);