Finite Group DatabasebetaFinite Group Databasebeta| order | 19188 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×Dic123 |
| unambiguous semidirect product | C3⋊(C13⋊C3×Dic41) |
| unambiguous semidirect product | (C13×Dic123)⋊C3 |
| derived | C3×C13×C41 ⋊ C3×C4 |
| Hall | C3×C13⋊C3×C41 ⋊ C4 |
| Hall | C13×C41 ⋊ C3×Dic3 |
| Hall | C3×C13⋊C3 ⋊ Dic41 |
| Sylow | C41 ⋊ Dic3×C13⋊C3 |
| Sylow | C13 ⋊ C3×Dic123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C13⋊C3×D123 |
| commutator, hypocenter | C3×C13×C41 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C13×C41 | C2×C3 |
| prime radical | C2×C3×C13⋊C3×C41 | C2 |
| LCS | G ▷ C3×C13×C41 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6396 |
882 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19188, 60);