Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C127 ⋊ #333 |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,b^2=f,c^2=f,d^2=ef,b^a=bc,c^a=ce,c^b=cf,d^b=def,g^b=g^1261279 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #333×D127, C2×#22549624, #30637385, … |
| maximal normal subgroup of | #333×D127, C2×#22549624, #30637385, … |
| maximal quotient of | #30636555, #30636614, #30636790, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 297);