Finite Group DatabasebetaFinite Group Databasebeta| order | 32526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C139⋊C9)⋊D13 |
| derived, Hall | C13×C139 ⋊ C2×C9 |
| Hall | C13×C139⋊C9 ⋊ C2 |
| Hall | D1807 ⋊ C9 |
| Hall | C139⋊C9 ⋊ D13 |
| Sylow | C139 ⋊ C9×D13 |
| Sylow | C13 ⋊ D139⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C139⋊C3)⋊D13 |
| commutator, hypocenter | C13×C139 | C2×C9 |
| Fitting, socle, cosocle | C3×C13×C139 | C2×C3 |
| prime radical | C3×D1807 | C3 |
| LCS | G ▷ C13×C139 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16263 |
Polycyclic presentation:
2,3,13,139,3|b^3=e,c^a=c^12,d^a=d^138,d^b=d^96969 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32526, 21);