Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C137 ⋊ #478 |
102 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^136,g^b=g^136,e^c=ef971 conjugacy classes — view the full character table.
| maximal subgroup of | #478×D137, C2×#22577705, #31790573, … |
| maximal normal subgroup of | #478×D137, C2×#22577705, #31790573, … |
| maximal quotient of | #31780797, #31781034, #31781052, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 851);