Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | C2×#16810457 |
| Sylow | C53 ⋊ C2×M64 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16 | C2×D53 |
| commutator | C2×C53 | C22×C16 |
| Frattini | C16 | C22×D53 |
| Fitting | C22×C16×C53 | C2 |
| socle | C22×C53 | C2×C16 |
| hypercenter | C22×C16 | D53 |
| hypocenter | C53 | C2×M64 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C16 ◁ C22×C16 | |
112 conjugacy classes of subgroups.
1744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271780, #27271781, #27271782, … |
| maximal normal subgroup of | #27271780, #27271781, #27271782, … |
| maximal quotient of | C2×#20272849, C4×#16810457, C2×C22⋊#13133123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6802);