Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| 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=df1682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36324105, #36324108, #36324516, … |
| maximal normal subgroup of | #36324105, #36324108, #36324516, … |
| maximal quotient of | #36322529, #36322555, #36322581, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 554);