Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C137 ⋊ #462 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=f,b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^136,e^c=ef971 conjugacy classes — view the full character table.
| maximal subgroup of | #462×D137, C2×#22577611, #31790240, … |
| maximal normal subgroup of | #462×D137, C2×#22577611, #31790240, … |
| maximal quotient of | #31780169, #31780173, #31780181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 757);