Finite Group DatabasebetaFinite Group Databasebeta| order | 19188 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#14523823⋊C3) |
| unambiguous semidirect product | (C3⋊#14523823)⋊C3 |
| Fitting, socle, derived | C3×C13×C41 ⋊ C3×C4 |
| Hall | C3×C13⋊C3×C41 ⋊ C4 |
| Hall | C13×C41 ⋊ C3×Dic3 |
| Hall | C3×C13⋊C3 ⋊ Dic41 |
| Sylow | C41 ⋊ C3⋊AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×Dic123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C41 | C3×C4 |
| prime radical | C3×C41×D13⋊C3 | C2 |
| cosocle | C3×D13×C41 | C2×C3 |
| LCS | G ▷ C3×C13×C41 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1599 |
Polycyclic presentation:
2,3,2,3,13,41|a^2=c,d^a=d^2,e^a=e^5,f^a=f^40,e^b=e^3,e^c=e^12501 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19188, 84);