Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#19128758 |
| Fitting | C2×M16×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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 | #36323942, C4×#19128758, #36323947, … |
| maximal normal subgroup of | #36323942, C4×#19128758, #36323947, … |
| maximal quotient of | C2×#24922996, C2×#24922999, #36322518, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 561);