Finite Group DatabasebetaFinite Group Databasebeta| order | 31518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(D103⋊C9) |
| unambiguous semidirect product | (C103⋊C9)⋊D17 |
| unambiguous semidirect product | D1751⋊C9 |
| derived, Hall | C17×C103 ⋊ C2×C9 |
| Hall | C17×C103⋊C9 ⋊ C2 |
| Hall | D1751 ⋊ C9 |
| Hall | C103⋊C9 ⋊ D17 |
| Sylow | C103 ⋊ C9×D17 |
| Sylow | C17 ⋊ D103⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C17⋊(D103⋊C3) |
| commutator, hypocenter | C17×C103 | C2×C9 |
| Fitting, socle, cosocle | C3×C17×C103 | C2×C3 |
| prime radical | C3×D1751 | C3 |
| LCS | G ▷ C17×C103 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15759 |
Polycyclic presentation:
2,3,17,103,3|b^3=e,c^a=c^16,d^a=d^102,d^b=d^56957 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31518, 17);