Finite Group DatabasebetaFinite Group Databasebeta| order | 19197 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C9 |
No aliases for this group.
| Fitting | C79×C9⋊C9 ⋊ C3 |
| Sylow | C79 ⋊ #6896 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C79⋊C3 |
| commutator, socle, cosocle | C32×C79 | C33 |
| Fitting | C79×C9⋊C9 | C3 |
| prime radical | C32×C79⋊C3 | C32 |
| hypercenter | C9⋊C9 | C79⋊C3 |
| hypocenter | C79 | #6896 |
| LCS | G ▷ C32×C79 ▷ C79 | |
| UCS | C1 ◁ C32 ◁ C9⋊C9 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6399 |
Polycyclic presentation:
3^5,79|b^3=e,c^3=d,b^a=bd,c^a=ce,f^a=f^55,f^b=f^55,f^c=f^23909 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19197, 211);