Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C137 ⋊ #487 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=f,b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^b=g^136,g^c=g^136974 conjugacy classes — view the full character table.
| maximal subgroup of | #31779938, #31779939, #31779945, … |
| maximal normal subgroup of | #31779938, #31779939, #31779945, … |
| maximal quotient of | #31780916, #31781468, #31781592, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 899);