Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #127×C137 ⋊ C2 |
| Sylow | C137 ⋊ #453 |
168 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=ef,g^b=g^136,d^c=df968 conjugacy classes — view the full character table.
| maximal subgroup of | #31778933, #31778935, #31782773, … |
| maximal normal subgroup of | #31778933, #31778935, #31782773, … |
| maximal quotient of | #31779706, #31779711, #31779733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 716);