Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C137 ⋊ #491 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=f,b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,c^b=cf,g^c=g^136968 conjugacy classes — view the full character table.
| maximal subgroup of | #491×D137, C2×#22577770, #31791131, … |
| maximal normal subgroup of | #491×D137, C2×#22577770, #31791131, … |
| maximal quotient of | #31780921, #31781476, #31781477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 916);