Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C337 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,d^2=e,b^a=bc,f^a=f^148,f^b=f^336,f^d=f^336692 conjugacy classes — view the full character table.
| maximal subgroup of | #36342156, #36342157, #36342158, … |
| maximal normal subgroup of | #36342156, #36342157, #36342158, … |
| maximal quotient of | #36342149, #36342151, #36342153, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 203);