Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C137 ⋊ C4 |
| Sylow | C137 ⋊ #327 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,c^2=f,b^a=bc,c^a=ce,g^a=g^100,c^b=cf,d^b=def,g^b=g^136,g^d=g^136359 conjugacy classes — view the full character table.
| maximal subgroup of | D137⋊#327, C2×#22578255, #31796162, … |
| maximal normal subgroup of | D137⋊#327, C2×#22578255, #31796162, … |
| maximal quotient of | #31795606, #31795607, #31795662, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1401);