Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#14582115 |
| unambiguous semidirect product | (C2×#14582115)⋊C2 |
| Fitting | C22×C337 ⋊ C8 |
| 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^85,f^d=f^148,f^e=f^336188 conjugacy classes — view the full character table.
| maximal subgroup of | #36342390, #36342391, C2×C22⋊#14582115, … |
| maximal normal subgroup of | #36342390, #36342391, C2×C22⋊#14582115, … |
| maximal quotient of | #36342390, #36342391, D4⋊#14582115, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 238);