Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16861133 |
| Sylow | C127 ⋊ C2×#103 |
162 conjugacy classes of subgroups.
1288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#16861133, #103×Dic127, #30638560, … |
| maximal normal subgroup of | C4×#16861133, #103×Dic127, #30638560, … |
| maximal quotient of | C2×Q8⋊(C127⋊C8), #30637133, #30637159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 540);