Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C137 ⋊ C4 |
| Sylow | C137 ⋊ #339 |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^37,g^b=g^100,g^d=g^136,g^e=g^136368 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22578275, #31796471, #104×#10587739, … |
| maximal normal subgroup of | C2×#22578275, #31796471, #104×#10587739, … |
| maximal quotient of | #31795616, #31795622, #31795623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1421);