Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×C22⋊C4×D127 |
| Fitting | C2×C22⋊C4×C127 ⋊ C2 |
| Sylow | C127 ⋊ C22×C22⋊C4 |
674 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 207 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #323×D127, #30637055, #342×D127, … |
| maximal normal subgroup of | #323×D127, #30637055, #342×D127, … |
| maximal quotient of | C2×#95×D127, C4×C22⋊C4×D127, C2×#22549723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 995);