Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C137 ⋊ C8 |
| Sylow | C137 ⋊ #324 |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,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 | #31797816, #31797817, #31797825, … |
| maximal normal subgroup of | #31797816, #31797817, #31797825, … |
| maximal quotient of | #31797789, #31797798, #31797822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1635);