Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#19128861 |
| Fitting | C2×SD16×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 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.
1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19128861, #36332960, #36332974, … |
| maximal normal subgroup of | C4×#19128861, #36332960, #36332974, … |
| maximal quotient of | C2×#24923276, C2×#24923267, C2×#24923308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1340);