Finite Group DatabasebetaFinite Group Databasebeta| order | 36738 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((D157⋊C3)⋊C13) |
| unambiguous semidirect product | (C3⋊(D157⋊C3))⋊C13 |
| unambiguous semidirect product | ((C157⋊C3)⋊C13)⋊D3 |
| unambiguous semidirect product | (C3⋊(D157⋊C13))⋊C3 |
| Fitting, socle, derived | C3×C157 ⋊ C2×C3×C13 |
| Hall | C3×(C157⋊C3)⋊C13 ⋊ C2 |
| Hall | C3⋊(D157⋊C3) ⋊ C13 |
| Hall | C157⋊C13 ⋊ C3×D3 |
| Hall | C3×C157⋊C3 ⋊ C2×C13 |
| Sylow | C157 ⋊ C3×D3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C157 | C2×C3×C13 |
| LCS | G ▷ C3×C157 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 471 |
Polycyclic presentation:
2,3,13,3,157|d^a=d^2,e^a=e^156,e^b=e^12,e^c=e^130123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36738, 33);