Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C167 ⋊ #341 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^1662684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322153, #36322154, #36322156, … |
| maximal normal subgroup of | #36322153, #36322154, #36322156, … |
| maximal quotient of | #36321973, #36321975, #36322000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 314);