Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q16×Dic127 |
| Sylow | C127 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
910 conjugacy classes — view the full character table.
| maximal subgroup of | #30640579, SD32×Dic127, #30640586, … |
| maximal normal subgroup of | #30640579, SD32×Dic127, #30640586, … |
| maximal quotient of | Q16×C127⋊C8, #30637581, #30637627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 644);