Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C167 ⋊ C2 |
| Sylow | C167 ⋊ #508 |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^166,d^b=de,e^b=ef,g^b=g^166,g^c=g^166935 conjugacy classes — view the full character table.
| maximal subgroup of | #36326446, #36326448, #36326452, … |
| maximal normal subgroup of | #36326446, #36326448, #36326452, … |
| maximal quotient of | #36325844, #36325919, #36325984, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 982);