Finite Group DatabasebetaFinite Group Databasebeta| order | 32058 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C13⋊C3)⋊D137) |
| unambiguous semidirect product | (C13⋊C3)⋊D411 |
| unambiguous semidirect product | C137⋊(C3⋊(D13⋊C3)) |
| unambiguous semidirect product | D5343⋊C3 |
| Fitting, socle, derived | C3×C13×C137 ⋊ C2×C3 |
| Hall | C3×C13⋊C3×C137 ⋊ C2 |
| Hall | C13×C137 ⋊ C3×D3 |
| Sylow | C137 ⋊ C3⋊(D13⋊C3) |
| Hall | C3×C13⋊C3 ⋊ D137 |
| Sylow | C13 ⋊ C3×D411 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C137 | C2×C3 |
| LCS | G ▷ C3×C13×C137 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5343 |
Polycyclic presentation:
2,3^2,13,137|c^a=c^2,d^a=d^12,e^a=e^136,d^b=d^31443 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32058, 18);