Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q16×#6157 |
| unambiguous semidirect product | D53⋊(C4×Q16) |
| Fitting | C2×Q16×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
238 conjugacy classes — view the full character table.
| maximal subgroup of | #358×#6157, #28310671, #362×#6157, … |
| maximal normal subgroup of | #358×#6157, #28310671, #362×#6157, … |
| maximal quotient of | C2×Q16×#88324, C2×#20290302, Q16×D53⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21259);