Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#13062438 |
| unambiguous semidirect product | D337⋊C42 |
| Fitting | C2×C4×C337 ⋊ C4 |
| derived, Sylow | C337 ⋊ C2×C42 |
108 conjugacy classes of subgroups.
704 conjugacy classes — view the full character table.
| maximal subgroup of | #36342170, #36342175, #36342177, … |
| maximal normal subgroup of | #36342170, #36342175, #36342177, … |
| maximal quotient of | C42×#13062438, C2×(C2×#13062438)⋊C4, #36342241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 222);