Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D8×Dic127 |
| Sylow | C127 ⋊ C4×D8 |
134 conjugacy classes of subgroups.
910 conjugacy classes — view the full character table.
| maximal subgroup of | #30640574, D16×Dic127, SD32×Dic127, … |
| maximal normal subgroup of | #30640574, D16×Dic127, SD32×Dic127, … |
| maximal quotient of | D8×C127⋊C8, #30637560, #30637615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 632);