Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C137 ⋊ #501 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=d,c^2=e,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^136,c^b=cf,g^c=g^136968 conjugacy classes — view the full character table.
| maximal subgroup of | #31780100, #31780102, #31780106, … |
| maximal normal subgroup of | #31780100, #31780102, #31780106, … |
| maximal quotient of | #31780958, #31781524, #31781529, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 959);