Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C137 ⋊ #324 |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^136,d^b=de1382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31778720, #31778721, #31778722, … |
| maximal normal subgroup of | #31778720, #31778721, #31778722, … |
| maximal quotient of | #31778612, #31778632, #31778729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 275);