Finite Group DatabasebetaFinite Group Databasebeta| order | 6859 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C192 · Schur multiplier (H2) = C192 |
| unitriangular | UT(3,𝔽19) |
| extraspecial | 19+1+2 |
| Heisenberg | H(3,𝔽19) |
| unambiguous semidirect product | C192⋊C19 |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle | C19 | C192 |
| LCS | G ▷ C19 ▷ C1 | |
| UCS | C1 ◁ C19 ◁ G | |
| LECS | G ▷ C19 ▷ C1 | |
43 conjugacy classes of subgroups.
Polycyclic presentation:
19^3|b^a=bc379 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6859, 3);