Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C137 ⋊ #416 |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^136,d^b=df1388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31780624, #31780627, #31780631, … |
| maximal normal subgroup of | #31780624, #31780627, #31780631, … |
| maximal quotient of | #31779171, #31779197, #31779223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 545);