Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C127 ⋊ #450 |
188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 188 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=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^126,d^b=df1279 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30637651, #30637652, #30637656, … |
| maximal normal subgroup of | #30637651, #30637652, #30637656, … |
| maximal quotient of | #30637682, #30637699, #30637750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 700);