Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q16×C127 ⋊ C2 |
| Sylow | C127 ⋊ #464 |
112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,127|b^2=df,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^126,g^b=g^126,e^c=ef901 conjugacy classes — view the full character table.
| maximal subgroup of | #464×D127, C2×#22550100, #30648181, … |
| maximal normal subgroup of | #464×D127, C2×#22550100, #30648181, … |
| maximal quotient of | #30638148, #30638162, #30638176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 773);