Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C137 ⋊ C2 |
| Sylow | C137 ⋊ #486 |
118 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,g^b=g^136,g^c=g^136974 conjugacy classes — view the full character table.
| maximal subgroup of | #31779878, #31779879, #31779885, … |
| maximal normal subgroup of | #31779878, #31779879, #31779885, … |
| maximal quotient of | #31780916, #31781471, #31781594, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 897);