Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×Q8×C137 ⋊ C2 |
| Sylow | C137 ⋊ #448 |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^136,d^b=df1379 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31779739, #31779740, #31779750, … |
| maximal normal subgroup of | #31779739, #31779740, #31779750, … |
| maximal quotient of | #31779712, #31779729, #31779780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 688);