Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#407 ⋊ C2 |
| Sylow | C53 ⋊ #2973 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C53×#407 | C2 |
| hypercenter | #407 | D53 |
| hypocenter | C53 | #2973 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #407 | |
456 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,f^2=g,b^a=be,c^a=cg,d^a=de,c^b=ce,h^b=h^52772 conjugacy classes — view the full character table.
| maximal subgroup of | #27278100, #27278103, #27279058, … |
| maximal normal subgroup of | #27278100, #27278103, #27279058, … |
| maximal quotient of | #27382768, #27382780, #27382827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13537);