Finite Group DatabasebetaFinite Group Databasebeta| order | 38532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2×C13 |
| unambiguous semidirect product | C22⋊(C19⋊#92789) |
| unambiguous semidirect product | C19⋊(C22⋊#92789) |
| Fitting, socle, derived, Hall | C22×C132×C19 ⋊ C3 |
| Hall | C132×C19 ⋊ A4 |
| Hall | C22×C132 ⋊ C19⋊C3 |
| Sylow | C132 ⋊ C22⋊(C19⋊C3) |
| Hall | C22×C19 ⋊ #92789 |
| Sylow | C19 ⋊ C22⋊#92789 |
| Sylow | C22 ⋊ C19⋊#92789 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C132×C19 | C3 |
| LCS | G ▷ C22×C132×C19 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1482 |
Polycyclic presentation:
3,2^2,13^2,19|b^a=c,c^a=bc,d^a=d^3,e^a=e^9,f^a=f^74284 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38532, 404);