Finite Group DatabasebetaFinite Group Databasebeta| order | 17748 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D87⋊D51 |
| Fitting, socle, derived, Hall | C32×C17×C29 ⋊ C22 |
| Hall | C17×C29 ⋊ D32 |
| Hall | C32×C29 ⋊ C2×D17 |
| Hall | C32×C17 ⋊ C2×D29 |
| Sylow | C29 ⋊ D3×D51 |
| Sylow | C17 ⋊ (C3⋊D3)⋊D29 |
| Sylow | C32 ⋊ D17×D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C17×C29 | C22 |
| LCS | G ▷ C32×C17×C29 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2958 |
Polycyclic presentation:
2^2,3^2,17,29|d^a=d^2,f^a=f^28,c^b=c^2,d^b=d^2,e^b=e^161173 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17748, 86);