Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C127 ⋊ #499 |
86 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,b^2=df,c^2=e,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^1262038 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30636781, #30636783, #30636790, … |
| maximal normal subgroup of | #30636781, #30636783, #30636790, … |
| maximal quotient of | #30638894, #30639458, #30639463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 951);