Finite Group DatabasebetaFinite Group Databasebeta| order | 9999 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C3×C4×C5×C25 (order 6000) · Inn(G) = C1 · Out(G) = C22×C3×C4×C5×C25 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C9999 |
| abelian | C9×C11×C101 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C3×C11×C101 |
| socle, prime radical | C3×C11×C101 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12 conjugacy classes of subgroups.
9999 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9999, 1);