Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C23×C137 ⋊ C8 |
| Sylow | C137 ⋊ #323 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,d^2=f,b^a=bc,c^a=ce,g^a=g^127,d^b=de,g^d=g^100,g^f=g^136158 conjugacy classes — view the full character table.
| maximal subgroup of | #31797814, #31797815, #31797827, … |
| maximal normal subgroup of | #31797814, #31797815, #31797827, … |
| maximal quotient of | #31797788, #31797790, #31797798, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1634);