Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | #405×D53 |
| Fitting | C53×#405 ⋊ C2 |
| Sylow | C53 ⋊ C2×#405 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D53 |
| commutator | C2×C53 | C22×C42 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#405 | C2 |
| socle | C22×C53 | C23×C4 |
| hypercenter | #405 | D53 |
| hypocenter | C53 | C2×#405 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ #405 | |
592 conjugacy classes of subgroups.
1120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1378, D53×#1379, #27298963, … |
| maximal normal subgroup of | D53×#1378, D53×#1379, #27298963, … |
| maximal quotient of | C8×M16×D53, D53×#1450, D53×#1451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12920);