Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#19128840 |
| Fitting | C2×M16×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#131 |
266 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323937, #36323972, #36323974, … |
| maximal normal subgroup of | #36323937, #36323972, #36323974, … |
| maximal quotient of | C2×#24923226, C2×#24923227, C4×#19128840, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1313);