Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C137 ⋊ #467 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=f,b^2=df,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^1362198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31778800, #31778802, #31778806, … |
| maximal normal subgroup of | #31778800, #31778802, #31778806, … |
| maximal quotient of | #31780154, #31780159, #31780188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 790);