Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #101×C137 ⋊ C2 |
| Sylow | C137 ⋊ #413 |
150 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,c^2=f,e^2=f,b^a=bd,d^a=df,e^b=ef,g^b=g^136,g^c=g^136770 conjugacy classes — view the full character table.
| maximal subgroup of | #31782471, #31782473, #31782479, … |
| maximal normal subgroup of | #31782471, #31782473, #31782479, … |
| maximal quotient of | #31779102, #31779106, #31779122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 532);