Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C137 ⋊ C2×C4⋊C8 |
138 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,b^2=d,e^2=f,b^a=bd,g^a=g^100,g^c=g^136,g^e=g^136584 conjugacy classes — view the full character table.
| maximal subgroup of | #31795618, #31795624, #31795653, … |
| maximal normal subgroup of | #31795618, #31795624, #31795653, … |
| maximal quotient of | #31796331, #31796334, #31796337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1550);