Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C137 ⋊ #430 |
102 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,b^2=d,d^2=f,e^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 | #31796746, #31796747, #31796750, … |
| maximal normal subgroup of | #31796746, #31796747, #31796750, … |
| maximal quotient of | #31796340, #31796341, #31796342, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1564);