Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C127 ⋊ C2 |
| Sylow | C127 ⋊ #349 |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,d^2=e,e^2=f,b^a=bc,c^a=cf,d^b=df,g^b=g^1261282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #349×D127, C2×#22549657, #30640349, … |
| maximal normal subgroup of | #349×D127, C2×#22549657, #30640349, … |
| maximal quotient of | #30636653, #30636669, #30636687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 330);