Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #101×C167 ⋊ C2 |
| Sylow | C167 ⋊ #413 |
150 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=e,c^2=f,e^2=f,b^a=bd,d^a=df,e^b=ef,g^b=g^166,g^c=g^166935 conjugacy classes — view the full character table.
| maximal subgroup of | #36325820, #36325822, #36325828, … |
| maximal normal subgroup of | #36325820, #36325822, #36325828, … |
| maximal quotient of | #36322451, #36322455, #36322471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 532);