Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#17984031 |
| Fitting | C2×Q16×C137 ⋊ C2 |
| Sylow | C137 ⋊ C2×SD32 |
90 conjugacy classes of subgroups.
974 conjugacy classes — view the full character table.
| maximal subgroup of | #31782638, C4×#17984031, #31782651, … |
| maximal normal subgroup of | #31782638, C4×#17984031, #31782651, … |
| maximal quotient of | C2×#22577203, C2×#22577207, C2×#22577230, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 972);