Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C24×C137 ⋊ C4 |
| Sylow | C137 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^100,d^b=de,d^c=df,g^d=g^136557 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22578303, D137⋊AΣL(1,𝔽16), #31797040, … |
| maximal normal subgroup of | C2×#22578303, D137⋊AΣL(1,𝔽16), #31797040, … |
| maximal quotient of | #31795713, #31795734, #31795767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1449);