Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C167 ⋊ #347 |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,g^a=g^166,c^b=cf1682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322170, #36322171, #36322172, … |
| maximal normal subgroup of | #36322170, #36322171, #36322172, … |
| maximal quotient of | #36322059, #36322218, C2×#24923047 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 327);