Finite Group DatabasebetaFinite Group Databasebeta| order | 38532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | ((C13⋊C3)⋊D13)⋊D19 |
| unambiguous semidirect product | ((C13⋊C3)⋊D19)⋊D13 |
| Fitting, socle, derived, Hall | C132×C19 ⋊ C22×C3 |
| Hall | (C13⋊D13)⋊D19 ⋊ C3 |
| Hall | C13×C19×C13⋊C3 ⋊ C22 |
| Hall | C13×C13⋊C3 ⋊ C2×D19 |
| Sylow | C132 ⋊ C2×C3×D19 |
| Sylow | C19 ⋊ D13×D13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C19 | C22×C3 |
| LCS | G ▷ C132×C19 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1482 |
Polycyclic presentation:
2^2,3,13^2,19|d^a=d^12,f^a=f^18,d^b=d^12,e^b=e^12,e^c=e^3514 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38532, 201);