Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C137 ⋊ #356 |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=f,c^2=f,d^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^100,c^b=cf,d^b=def,g^b=g^136,d^c=df,g^d=g^136557 conjugacy classes — view the full character table.
| maximal subgroup of | #31795924, #31795925, #31795926, … |
| maximal normal subgroup of | #31795924, #31795925, #31795926, … |
| maximal quotient of | #31795720, #31795731, #31795774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1460);