Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | #387×D53 |
| Fitting | C53×#387 ⋊ C2 |
| Sylow | C53 ⋊ C2×#387 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D53 |
| commutator | C22×C53 | C23×C4 |
| Fitting | C53×#387 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | #387 | D53 |
| hypocenter | C53 | C2×#387 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #387 | |
712 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#387×D53, D53×#2290, D53×#2295, … |
| maximal normal subgroup of | C2×#387×D53, D53×#2290, D53×#2295, … |
| maximal quotient of | D53×#1434, D53×#1436, #27305264, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6930);