Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C167 ⋊ #461 |
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,167|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^166,e^c=ef1181 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #461×D167, C2×#24923472, #36333589, … |
| maximal normal subgroup of | #461×D167, C2×#24923472, #36333589, … |
| maximal quotient of | #36323511, #36323515, #36323525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 752);