Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#19128759 |
| Sylow | C167 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19128759, #104×Dic167, #36323948, … |
| maximal normal subgroup of | C4×#19128759, #104×Dic167, #36323948, … |
| maximal quotient of | C2×D4⋊(C167⋊C8), C2×Q8⋊(C167⋊C8), #36322520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 562);