Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16861136 |
| Sylow | C127 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#16861136, #104×Dic127, #30638540, … |
| maximal normal subgroup of | C4×#16861136, #104×Dic127, #30638540, … |
| maximal quotient of | C2×D4⋊(C127⋊C8), C2×Q8⋊(C127⋊C8), #30637112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 562);