Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊Q8×C167 ⋊ C2 |
| Sylow | C167 ⋊ #543 |
242 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 242 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|a^2=f,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,g^d=g^1661184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323059, #36323062, #36323093, … |
| maximal normal subgroup of | #36323059, #36323062, #36323093, … |
| maximal quotient of | #36326749, #36326751, #36326865, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1174);