Finite Group DatabasebetaFinite Group Databasebeta| order | 32058 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D5343 |
| unambiguous semidirect product | C13⋊(C3⋊D411) |
| unambiguous semidirect product | C137⋊(C3⋊D39) |
| Fitting, socle, derived, Hall | C32×C13×C137 ⋊ C2 |
| Hall | C13×C137 ⋊ C3⋊D3 |
| Hall | C32×C137 ⋊ D13 |
| Sylow | C137 ⋊ C3⋊D39 |
| Hall | C32×C13 ⋊ D137 |
| Sylow | C13 ⋊ C3⋊D411 |
| Sylow | C32 ⋊ D1781 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C13×C137 | C2 |
| LCS | G ▷ C32×C13×C137 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16029 |
Polycyclic presentation:
2,3^2,13,137|b^a=b^2,c^a=c^2,d^a=d^12,e^a=e^1368016 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32058, 32);