Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C7×C9×C16 (order 4032) · Inn(G) = C1 · Out(G) = C22×C7×C9×C16 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C8128 |
| abelian | C64×C127 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C32 | C2×C127 |
| socle | C2×C127 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
14 conjugacy classes of subgroups.
8128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1);