Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of Dic106 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C24×D212 |
| Fitting | C24×C4×C53 ⋊ C2 |
| Sylow | C53 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D53 |
| commutator | C2×C53 | C26 |
| Frattini | C2 | C25×D53 |
| Fitting | C24×C4×C53 | C2 |
| socle | C25×C53 | C22 |
| hypercenter | C24×C4 | D53 |
| hypocenter | C53 | C24×D4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C25 ◁ C24×C4 | |
10552 conjugacy classes of subgroups.
1744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#20272955, #27305961, #27306307, … |
| maximal normal subgroup of | C2×#20272955, #27305961, #27306307, … |
| maximal quotient of | C24×#11719921, C24×C4⋊Dic53, C23×C4×D212, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19303);