Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#17984119 |
| Fitting | C22×Q8×C137 ⋊ C2 |
| Sylow | C137 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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 | #31781155, #31781161, #31781259, … |
| maximal normal subgroup of | #31781155, #31781161, #31781259, … |
| maximal quotient of | C2×#22577412, C2×#22577402, C2×#22577443, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1342);