Finite Group DatabasebetaFinite Group Databasebeta| order | 9006 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C23×C3×C9×C13 (order 2808) · Inn(G) = C1 · Out(G) = C23×C3×C9×C13 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C9006 |
| abelian | C2×C3×C19×C79 |
| multiplicative | (ℤ/9007)ˣ, (ℤ/18014)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
16 conjugacy classes of subgroups.
9006 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9006, 1);