Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | #102×D127 |
| Fitting | #102×C127 ⋊ C2 |
| Sylow | C127 ⋊ C2×#102 |
202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 202 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.
910 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#102×D127, #416×D127, #418×D127, … |
| maximal normal subgroup of | C2×#102×D127, #416×D127, #418×D127, … |
| maximal quotient of | D4⋊C8×D127, #30637127, #30637153, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 534);