Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×M16×C167 ⋊ C2 |
| Sylow | C167 ⋊ #418 |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^166,c^b=cf,d^b=df,g^b=g^1661682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36324107, #36324109, #36324512, … |
| maximal normal subgroup of | #36324107, #36324109, #36324512, … |
| maximal quotient of | #36322530, #36322556, #36322582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 555);