Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #131×C167 ⋊ C2 |
| Sylow | C167 ⋊ #578 |
248 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=f,b^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^166,e^b=ef,g^b=g^166,d^c=df1682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36326100, #36326104, #36326114, … |
| maximal normal subgroup of | #36326100, #36326104, #36326114, … |
| maximal quotient of | #36332672, #36332738, #36332983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1366);