Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C127 ⋊ C2 |
| Sylow | C127 ⋊ #453 |
168 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^126,d^b=df,e^b=ef,d^c=df1087 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30640712, #30640724, #30640734, … |
| maximal normal subgroup of | #30640712, #30640724, #30640734, … |
| maximal quotient of | #30637648, #30637653, #30637676, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 717);