Finite Group DatabasebetaFinite Group Databasebeta| order | 8001 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C23×C32×C7×C9 (order 4536) · Inn(G) = C1 · Out(G) = C23×C32×C7×C9 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C8001 |
| abelian | C7×C9×C127 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C3 | C3×C7×C127 |
| socle | C3×C7×C127 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12 conjugacy classes of subgroups.
8001 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8001, 1);