Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×M16×C127 ⋊ C2 |
| Sylow | C127 ⋊ #421 |
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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,d^2=f,e^2=f,b^a=bd,d^a=df,c^b=cf,d^b=df,g^b=g^1261282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30638692, #30638693, #30638697, … |
| maximal normal subgroup of | #30638692, #30638693, #30638697, … |
| maximal quotient of | #30637115, #30637120, #30637124, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 565);