Finite Group DatabasebetaFinite Group Databasebeta| order | 32058 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C13⋊C9)⋊D137 |
| unambiguous semidirect product | C137⋊(D13⋊C9) |
| unambiguous semidirect product | D1781⋊C9 |
| derived, Hall | C13×C137 ⋊ C2×C9 |
| Hall | C13⋊C9×C137 ⋊ C2 |
| Hall | D1781 ⋊ C9 |
| Sylow | C137 ⋊ D13⋊C9 |
| Hall | C13⋊C9 ⋊ D137 |
| Sylow | C13 ⋊ C9×D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C13⋊C3)⋊D137 |
| commutator, hypocenter | C13×C137 | C2×C9 |
| Fitting, socle, cosocle | C3×C13×C137 | C2×C3 |
| prime radical | C3×D1781 | C3 |
| LCS | G ▷ C13×C137 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16029 |
Polycyclic presentation:
2,3,13,137,3|b^3=e,c^a=c^12,d^a=d^136,c^b=c^31452 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32058, 12);