Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C137 ⋊ #359 |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^100,c^b=ce,e^b=ef,g^b=g^136,g^d=g^136260 conjugacy classes — view the full character table.
| maximal subgroup of | D137⋊#359, C2×#22578318, #31797103, … |
| maximal normal subgroup of | D137⋊#359, C2×#22578318, #31797103, … |
| maximal quotient of | #31795744, #31795745, #31795780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1464);