Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×Q16×C167 ⋊ C2 |
| Sylow | C167 ⋊ #452 |
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 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,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,g^b=g^166,g^c=g^1661181 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #452×D167, C2×#24923430, #36333352, … |
| maximal normal subgroup of | #452×D167, C2×#24923430, #36333352, … |
| maximal quotient of | #36323100, #36323117, #36323168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 710);