Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C127 ⋊ #440 |
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 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=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^126,d^b=df1282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #440×D127, C2×#22549976, #30647527, … |
| maximal normal subgroup of | #440×D127, C2×#22549976, #30647527, … |
| maximal quotient of | #30637542, #30637587, #30637606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 649);