Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D8×C137 ⋊ C4 |
| Sylow | C137 ⋊ #443 |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^100,d^b=df,g^c=g^100,g^e=g^136266 conjugacy classes — view the full character table.
| maximal subgroup of | #31797188, #31797189, #31797191, … |
| maximal normal subgroup of | #31797188, #31797189, #31797191, … |
| maximal quotient of | D8×#11764047, #31796372, #31796377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1591);