Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×Q8×C167 ⋊ C2 |
| Sylow | C167 ⋊ #448 |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^166,d^b=df1679 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323088, #36323089, #36323099, … |
| maximal normal subgroup of | #36323088, #36323089, #36323099, … |
| maximal quotient of | #36323061, #36323078, #36323129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 688);