Finite Group DatabasebetaFinite Group Databasebeta| order | 6859 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2222316 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C19 |
| abelian | C19×C361 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C19 | C192 |
| socle | C192 | C19 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C19 ▷ C1 | |
42 conjugacy classes of subgroups.
6859 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C19×C361, C3×C19×C361 |
| maximal normal subgroup of | C2×C19×C361, C3×C19×C361 |
| maximal quotient of | C2×C19×C361, C3×C19×C361 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6859, 2);