Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #125×C137 ⋊ C2 |
| Sylow | C137 ⋊ #488 |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^136,g^b=g^136,g^c=g^136974 conjugacy classes — view the full character table.
| maximal subgroup of | #488×D137, C2×#22577760, #31791110, … |
| maximal normal subgroup of | #488×D137, C2×#22577760, #31791110, … |
| maximal quotient of | #31780919, #31781464, #31781471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 906);