Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | #520×D53 |
| Fitting | C53×#520 ⋊ C2 |
| Sylow | C53 ⋊ C2×#520 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D53 |
| commutator | C2×C53 | C24×C4 |
| Fitting | C53×#520 | C2 |
| socle | C22×C53 | C25 |
| hypercenter | #520 | D53 |
| hypocenter | C53 | C2×#520 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ #520 | |
1640 conjugacy classes of subgroups.
952 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1859, D53×#1860, #27384967, … |
| maximal normal subgroup of | D53×#1859, D53×#1860, #27384967, … |
| maximal quotient of | D53×#2274, D53×#2275, D53×#2276, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17702);