Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#17984014 |
| Fitting | C2×M16×C137 ⋊ C2 |
| Sylow | C137 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31780593, C4×#17984014, #31780598, … |
| maximal normal subgroup of | #31780593, C4×#17984014, #31780598, … |
| maximal quotient of | C2×#22577130, C2×#22577133, #31779169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 561);