Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C337 ⋊ C4 |
| Sylow | C337 ⋊ #107 |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,b^2=ce,c^2=e,b^a=bc,c^a=ce,f^a=f^148,f^d=f^336686 conjugacy classes — view the full character table.
| maximal subgroup of | #36342217, #36342218, #36342231, … |
| maximal normal subgroup of | #36342217, #36342218, #36342231, … |
| maximal quotient of | #36342168, #36342169, #36342179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 215);