Finite Group DatabasebetaFinite Group Databasebeta| order | 19197 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C81 · Schur multiplier (H2) = C3 |
| direct product | C3×C79⋊C81 |
| unambiguous semidirect product | (C3×C79)⋊C81 |
| derived, Sylow | C79 ⋊ C3×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C27 | C79⋊C3 |
| commutator, hypocenter | C79 | C3×C81 |
| Frattini | C27 | C3×C79⋊C3 |
| Fitting | C3×C27×C79 | C3 |
| socle, prime radical | C32×C79 | C27 |
| cosocle | C27×C79 | C32 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C3×C27 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19197 |
2349 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19197, 125);