Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C137 ⋊ #431 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,c^2=d,e^2=f,b^a=bd,g^a=g^100,g^e=g^136584 conjugacy classes — view the full character table.
| maximal subgroup of | #31795613, #31795615, #31795617, … |
| maximal normal subgroup of | #31795613, #31795615, #31795617, … |
| maximal quotient of | #31796503, C4×C22⋊#11764047, C4×C4⋊#11764047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1565);