Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#17984032 |
| Sylow | C137 ⋊ C2×SD32 |
90 conjugacy classes of subgroups.
974 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#17984032, #31782644, #31782650, … |
| maximal normal subgroup of | C4×#17984032, #31782644, #31782650, … |
| maximal quotient of | C2×#22577204, C2×#22577206, C2×#22577230, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 973);