Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | AGL(1,ℤ/8)×C167 ⋊ C2 |
| Sylow | C167 ⋊ #453 |
168 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,167|d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=ef,d^c=df,g^c=g^166929 conjugacy classes — view the full character table.
| maximal subgroup of | #453×D167, C2×#24923435, #36333484, … |
| maximal normal subgroup of | #453×D167, C2×#24923435, #36333484, … |
| maximal quotient of | #36323054, #36323059, #36323081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 715);