Finite Group DatabasebetaFinite Group Databasebeta| order | 19188 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14523824⋊C9 |
| derived, Hall | C13×C41 ⋊ C4×C9 |
| Hall | C41×C13⋊C9 ⋊ C4 |
| Hall | #14523824 ⋊ C9 |
| Hall | C13⋊C9 ⋊ #4223 |
| Sylow | C41 ⋊ Dic13⋊C9 |
| Sylow | C13 ⋊ C9×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #14523824⋊C3 |
| commutator, hypocenter | C13×C41 | C4×C9 |
| Fitting, socle | C3×C13×C41 | C3×C4 |
| prime radical, cosocle | C3×C13×D41 | C2×C3 |
| LCS | G ▷ C13×C41 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4797 |
Polycyclic presentation:
2,3,2,13,41,3|a^2=c,b^3=f,d^a=d^12,e^a=e^32,d^b=d^3,e^c=e^40258 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19188, 18);