Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #99×C127 ⋊ C2 |
| Sylow | C127 ⋊ #410 |
158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,127|a^2=e,c^2=f,b^a=bd,d^a=df,e^b=ef,g^c=g^126715 conjugacy classes — view the full character table.
| maximal subgroup of | #30640368, #30640370, #30640378, … |
| maximal normal subgroup of | #30640368, #30640370, #30640378, … |
| maximal quotient of | #30637041, #30637043, #30637049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 521);