Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C167 ⋊ #499 |
86 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,b^2=df,c^2=e,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^166,g^c=g^1661184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36326293, #36326294, #36326297, … |
| maximal normal subgroup of | #36326293, #36326294, #36326297, … |
| maximal quotient of | #36324301, #36324865, #36324869, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 950);