Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D8×C137 ⋊ C2 |
| Sylow | C137 ⋊ #472 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,e^c=ef,g^c=g^136968 conjugacy classes — view the full character table.
| maximal subgroup of | #31782743, #31782745, #31782750, … |
| maximal normal subgroup of | #31782743, #31782745, #31782750, … |
| maximal quotient of | #31780141, #31780146, #31780185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 816);