Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #137×C127 ⋊ C2 |
| Sylow | C127 ⋊ #456 |
142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=ef,d^c=df,g^c=g^126709 conjugacy classes — view the full character table.
| maximal subgroup of | #456×D127, C2×#22550057, #30648076, … |
| maximal normal subgroup of | #456×D127, C2×#22550057, #30648076, … |
| maximal quotient of | #30637690, #30637692, #30637697, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 730);