Finite Group DatabasebetaFinite Group Databasebeta| order | 19188 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D1599 |
| unambiguous semidirect product | (C2×C3)⋊(C3×D533) |
| unambiguous semidirect product | (C2×C41)⋊(C3×D39) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1599 |
| commutator, cosocle, hypocenter | C3×C13×C41 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C13×C41 | C2 |
| LCS | G ▷ C3×C13×C41 | |
| UCS | C1 ◁ C2×C3 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6396 |
4806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19188, 159);