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 ⋊ #2976 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C53×#407 | C2 |
| hypercenter | #407 | D53 |
| hypocenter | C53 | #2976 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #407 | |
412 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,f^2=g,b^a=be,d^a=de,h^a=h^52,c^b=ce,d^b=dg,h^b=h^52772 conjugacy classes — view the full character table.
| maximal subgroup of | #27278193, #27278197, #27278200, … |
| maximal normal subgroup of | #27278193, #27278197, #27278200, … |
| maximal quotient of | #27382789, #27382812, #27382870, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13560);