Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C137 ⋊ C2×#97 |
146 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,d^2=f,b^a=bf,g^a=g^100,g^c=g^136,g^d=g^136584 conjugacy classes — view the full character table.
| maximal subgroup of | #31795614, #31795666, #31795682, … |
| maximal normal subgroup of | #31795614, #31795666, #31795682, … |
| maximal quotient of | #31795985, #31795997, #31796003, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1508);