Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C137 ⋊ #357 |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^136,c^b=ce,e^b=ef974 conjugacy classes — view the full character table.
| maximal subgroup of | #357×D137, C2×#22577204, #31782493, … |
| maximal normal subgroup of | #357×D137, C2×#22577204, #31782493, … |
| maximal quotient of | #31778750, #31778798, #31778835, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 350);