Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#14582115 |
| Fitting | C4×C337 ⋊ C8 |
| 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^85,f^d=f^148,f^e=f^336188 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#14582115, Q8⋊#14582115, #36342394, … |
| maximal normal subgroup of | D4⋊#14582115, Q8⋊#14582115, #36342394, … |
| maximal quotient of | #36342394, #36342395, (C2×#14582115)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 239);