Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C137 ⋊ C2 |
| Sylow | C137 ⋊ #497 |
124 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=f,b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,c^b=cf,g^b=g^136968 conjugacy classes — view the full character table.
| maximal subgroup of | #31780094, #31780099, #31780104, … |
| maximal normal subgroup of | #31780094, #31780099, #31780104, … |
| maximal quotient of | #31780414, #31780421, #31780433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 941);