Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C137 ⋊ C2 |
| Sylow | C137 ⋊ #461 |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^136,e^c=ef,g^c=g^1361379 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31779969, #31779971, #31779990, … |
| maximal normal subgroup of | #31779969, #31779971, #31779990, … |
| maximal quotient of | #31780165, #31780179, #31780189, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 755);