Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊Q8×C127 ⋊ C2 |
| Sylow | C127 ⋊ #456 |
142 conjugacy classes of subgroups.
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,g^b=g^126,d^c=df898 conjugacy classes — view the full character table.
| maximal subgroup of | #30636883, #30636885, #30640751, … |
| maximal normal subgroup of | #30636883, #30636885, #30640751, … |
| maximal quotient of | #30637691, #30637698, #30637703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 731);