Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #117×C167 ⋊ C2 |
| Sylow | C167 ⋊ #421 |
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^166,c^b=cf,d^b=df,g^b=g^1661682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36324103, #36324104, #36324105, … |
| maximal normal subgroup of | #36324103, #36324104, #36324105, … |
| maximal quotient of | #36322526, #36322530, #36322534, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 567);