Finite Group DatabasebetaFinite Group Databasebeta| order | 19188 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic533⋊C9 |
| derived, Hall | C13×C41 ⋊ C4×C9 |
| Hall | C41×C13⋊C9 ⋊ C4 |
| Hall | Dic533 ⋊ C9 |
| Hall | C13⋊C9 ⋊ Dic41 |
| Sylow | C41 ⋊ Dic13⋊C9 |
| Sylow | C13 ⋊ C9×Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | (C13⋊C3)⋊D41 |
| commutator, hypocenter | C13×C41 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C13×C41 | C2×C3 |
| LCS | G ▷ C13×C41 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19188 |
Polycyclic presentation:
2,3,13,41,2,3|a^2=e,b^3=f,c^a=c^12,d^a=d^40,c^b=c^3888 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19188, 12);