Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C43×D53 |
| Fitting | C43×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D53 |
| commutator, hypocenter | C53 | C2×C43 |
| Frattini | C23 | C23×D53 |
| Fitting | C43×C53 | C2 |
| socle | C23×C53 | C24 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C43 | |
1272 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1276, #27273532, C42×C8×D53, … |
| maximal normal subgroup of | D53×#1276, #27273532, C42×C8×D53, … |
| maximal quotient of | C43×Dic53, C4×#95×D53, C4×#16810468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6831);