Finite Group DatabasebetaFinite Group Databasebeta| order | 6679 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C7×C9×C53 (order 6678) · Inn(G) = C1 · Out(G) = C2×C7×C9×C53 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C6679 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C1 | |
2 conjugacy classes of subgroups.
6679 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic6679, C2×D6679 |
| maximal subgroup of | D6679, C2×C6679, C6679⋊C3, … |
| maximal normal subgroup of | D6679, C2×C6679, C6679⋊C3, … |
| maximal quotient of | C2×C6679, C3×C6679, C5×C6679 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6679, 1);