Finite Group DatabasebetaFinite Group Databasebeta| order | 19197 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C27 · Schur multiplier (H2) = C33 |
| direct product | C32×C79⋊C27 |
| derived, Sylow | C79 ⋊ C32×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C9 | C79⋊C3 |
| commutator, hypocenter | C79 | C32×C27 |
| Frattini | C9 | C32×C79⋊C3 |
| Fitting | C32×C9×C79 | C3 |
| socle, prime radical | C33×C79 | C9 |
| cosocle | C9×C79 | C33 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C32×C9 | |
144 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, 235);