Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#19128827 |
| Fitting | C2×C4⋊C4×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#126 |
246 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 111 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 | #36322506, #36326688, C4×#19128827, … |
| maximal normal subgroup of | #36322506, #36326688, C4×#19128827, … |
| maximal quotient of | C2×#24923136, C2×#24923150, C2×#24923152, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1075);