Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C127 ⋊ #341 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^b=g^1261288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #341×D127, C2×#22549640, #30638455, … |
| maximal normal subgroup of | #341×D127, C2×#22549640, #30638455, … |
| maximal quotient of | #30636564, #30636566, #30636568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 313);