Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#17984152 |
| Fitting | C2×D4×C137 ⋊ C4 |
| Sylow | C137 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
368 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#17984152, #31796552, #31796564, … |
| maximal normal subgroup of | C4×#17984152, #31796552, #31796564, … |
| maximal quotient of | C2×D4⋊#11764047, C2×#22578253, #31796081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1543);