Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD32×C137 ⋊ C2 |
| Sylow | C137 ⋊ #509 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^136,d^b=de,e^b=ef,g^c=g^136764 conjugacy classes — view the full character table.
| maximal subgroup of | #509×D137, C2×#22577840, #31793922, … |
| maximal normal subgroup of | #509×D137, C2×#22577840, #31793922, … |
| maximal quotient of | #31782500, #31782503, #31782576, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 986);