Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #100×C137 ⋊ C2 |
| Sylow | C137 ⋊ #455 |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^136,d^b=df,e^b=ef,g^b=g^136,d^c=df764 conjugacy classes — view the full character table.
| maximal subgroup of | #31782780, #31782781, #31782791, … |
| maximal normal subgroup of | #31782780, #31782781, #31782791, … |
| maximal quotient of | #31779743, #31779748, #31779771, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 729);