Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #127×C167 ⋊ C2 |
| Sylow | C167 ⋊ #493 |
162 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|b^2=df,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^b=g^1661184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322300, #36323191, #36323192, … |
| maximal normal subgroup of | #36322300, #36323191, #36323192, … |
| maximal quotient of | #36323728, #36323743, #36323745, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 925);