Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22⋊Q8×C167 ⋊ C2 |
| Sylow | C167 ⋊ #536 |
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,167|b^2=e,c^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,g^b=g^166,g^d=g^1661184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36333410, #36333412, #36333428, … |
| maximal normal subgroup of | #36333410, #36333412, #36333428, … |
| maximal quotient of | #36326721, #36326727, #36326760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1122);