Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C137 ⋊ #328 |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=ce,g^a=g^136,c^b=cf,d^b=def971 conjugacy classes — view the full character table.
| maximal subgroup of | #328×D137, C2×#22577140, #31779274, … |
| maximal normal subgroup of | #328×D137, C2×#22577140, #31779274, … |
| maximal quotient of | #31778612, #31778615, #31778667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 286);