Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×#16810441 |
| Sylow | C53 ⋊ C2×C4⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×D53 |
| commutator | C2×C53 | C22×C16 |
| Frattini | C2×C8 | C22×D53 |
| Fitting | C22×C16×C53 | C2 |
| socle | C23×C53 | C2×C8 |
| hypercenter | C22×C16 | D53 |
| hypocenter | C53 | C2×C4⋊C16 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C8 ◁ C22×C16 | |
184 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271490, #27299396, C4×#16810441, … |
| maximal normal subgroup of | #27271490, #27299396, C4×#16810441, … |
| maximal quotient of | C2×#20272778, C2×#20272784, #27295690, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6262);