Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #108×C137 ⋊ C2 |
| Sylow | C137 ⋊ #473 |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=f,b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^136,e^c=ef,g^c=g^136968 conjugacy classes — view the full character table.
| maximal subgroup of | #31782761, #31782763, #31782768, … |
| maximal normal subgroup of | #31782761, #31782763, #31782768, … |
| maximal quotient of | #31780155, #31780160, #31780179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 825);