Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #103×C137 ⋊ C2 |
| Sylow | C137 ⋊ #489 |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^136,c^b=cf,g^c=g^136968 conjugacy classes — view the full character table.
| maximal subgroup of | #489×D137, C2×#22577764, #31791132, … |
| maximal normal subgroup of | #489×D137, C2×#22577764, #31791132, … |
| maximal quotient of | #31780921, #31781476, #31781481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 910);