Finite Group DatabasebetaFinite Group Databasebeta| order | 38532 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C3⋊(C19⋊#10621725) |
| unambiguous semidirect product | C19⋊(C3⋊#10621725) |
| derived, Hall | C3×C132×C19 ⋊ C4 |
| Hall | C132×C19 ⋊ Dic3 |
| Hall | C3×C132 ⋊ Dic19 |
| Sylow | C132 ⋊ Dic57 |
| Hall | C3×C19 ⋊ #10621725 |
| Sylow | C19 ⋊ C3⋊#10621725 |
| Sylow | C3 ⋊ C19⋊#10621725 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C13⋊D247) |
| commutator, hypocenter | C3×C132×C19 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C132×C19 | C2 |
| LCS | G ▷ C3×C132×C19 | |
| UCS | C1 ◁ C2 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 38532 |
Polycyclic presentation:
2,3,13^2,19,2|a^2=f,b^a=b^2,c^a=c^12,d^a=d^12,e^a=e^189636 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38532, 142);