Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×#13133123 |
| derived, Sylow | C53 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D53 |
| commutator, hypocenter | C53 | C22×C32 |
| Frattini | C16 | C22×D53 |
| Fitting | C22×C16×C53 | C2 |
| socle | C23×C53 | C16 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22×C16 | |
120 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271778, #27271779, #27271790, … |
| maximal normal subgroup of | #27271778, #27271779, #27271790, … |
| maximal quotient of | C2×C4×#13133123, C2×C22⋊#13133123, C2×C4⋊#13133123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6799);