Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#13062438 |
| unambiguous semidirect product | D337⋊(C22⋊C4) |
| unambiguous semidirect product | (C2×#13062438)⋊C22 |
| Fitting | C23×C337 ⋊ C4 |
| Sylow | C337 ⋊ C2×C22⋊C4 |
132 conjugacy classes of subgroups.
692 conjugacy classes — view the full character table.
| maximal subgroup of | #36342182, #36342183, C4×C22⋊#13062438, … |
| maximal normal subgroup of | #36342182, #36342183, C4×C22⋊#13062438, … |
| maximal quotient of | C2×(C2×#13062438)⋊C4, C4×C22⋊#13062438, #36342246, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 223);