Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#17984185 |
| Sylow | C137 ⋊ C2×M32 |
90 conjugacy classes of subgroups.
176 conjugacy classes — view the full character table.
| maximal subgroup of | #31797864, #31797868, #31797869, … |
| maximal normal subgroup of | #31797864, #31797868, #31797869, … |
| maximal quotient of | C2×#22578497, C4×#17984185, C2×#22578500, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1669);