Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×(C2×D167)⋊C8 |
| Fitting | C22×C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322061, #36323895, C4×(C2×D167)⋊C8, … |
| maximal normal subgroup of | #36322061, #36323895, C4×(C2×D167)⋊C8, … |
| maximal quotient of | C2×#24922992, C2×#24922994, #36322450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 509);