Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×Q8×C127 ⋊ C2 |
| Sylow | C127 ⋊ #448 |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|b^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 | #30637680, #30637681, #30637691, … |
| maximal normal subgroup of | #30637680, #30637681, #30637691, … |
| maximal quotient of | #30637653, #30637670, #30637721, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 688);