Finite Group DatabasebetaFinite Group Databasebeta| order | 19197 |
| automorphism | ? |
| homology | Abelianization (H1) = C92 · Schur multiplier (H2) = C33 |
| unambiguous semidirect product | C79⋊#6855 |
| Sylow | C79 ⋊ #6855 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C33 | C3×C79⋊C3 |
| commutator | C3×C79 | C92 |
| Fitting | C32×C9×C79 | C3 |
| socle, prime radical, cosocle | C33×C79 | C32 |
| hypercenter | C32×C9 | C79⋊C3 |
| hypocenter | C79 | #6855 |
| LCS | G ▷ C3×C79 ▷ C79 | |
| UCS | C1 ◁ C33 ◁ C32×C9 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19197 |
Polycyclic presentation:
3^5,79|a^3=d,b^3=e,b^a=bc,f^b=f^232205 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19197, 69);