Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#16861123 |
| Fitting | C2×C22⋊C4×C127 ⋊ C2 |
| Sylow | C127 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30638517, C4×#16861123, #30638643, … |
| maximal normal subgroup of | #30638517, C4×#16861123, #30638643, … |
| maximal quotient of | C2×#22549599, C2×#22549601, #30637046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 519);