Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#17984003 |
| Sylow | C137 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31778907, #31778908, #31778913, … |
| maximal normal subgroup of | #31778907, #31778908, #31778913, … |
| maximal quotient of | C2×#22577127, C2×#22577129, #31779107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 520);