Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q16×C137 ⋊ C2 |
| Sylow | C137 ⋊ #470 |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=f,b^2=df,d^2=f,b^a=bd,c^a=ce,d^a=df,c^b=cf,g^c=g^136968 conjugacy classes — view the full character table.
| maximal subgroup of | #31782738, #31783007, #470×D137, … |
| maximal normal subgroup of | #31782738, #31783007, #470×D137, … |
| maximal quotient of | #31780275, #31780280, #31780309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 804);