Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C137 ⋊ C4 |
| Sylow | C137 ⋊ #428 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,g^a=g^100,c^b=cf,g^e=g^136362 conjugacy classes — view the full character table.
| maximal subgroup of | #31796744, #31796745, #31796748, … |
| maximal normal subgroup of | #31796744, #31796745, #31796748, … |
| maximal quotient of | #31796340, #31796341, #31796342, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1560);