Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C167 ⋊ #543 |
242 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=f,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,g^c=g^1661682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323060, #36323063, #36323094, … |
| maximal normal subgroup of | #36323060, #36323063, #36323094, … |
| maximal quotient of | #36326750, #36326752, #36326866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1175);