Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C137 ⋊ #349 |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,d^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^100,d^b=df,g^d=g^136566 conjugacy classes — view the full character table.
| maximal subgroup of | #31795721, #31795722, #31795723, … |
| maximal normal subgroup of | #31795721, #31795722, #31795723, … |
| maximal quotient of | #31795709, #31795725, #31795741, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1445);