Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#14582113 |
| Sylow | C337 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^148,f^d=f^336692 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#14582113, #36342153, Q8⋊#14582113, … |
| maximal normal subgroup of | D4⋊#14582113, #36342153, Q8⋊#14582113, … |
| maximal quotient of | #36342166, #36342168, #36342171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 212);