Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ C4⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C2×#6157 |
| commutator | C2×C53 | C2×C32 |
| Fitting | C2×C16×C53 | C4 |
| socle | C22×C53 | C2×C16 |
| hypercenter | C2×C16 | #6157 |
| hypocenter | C53 | C4⋊C32 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^30,h^b=h^52,h^d=h^52496 conjugacy classes — view the full character table.
| maximal subgroup of | #28299119, #28299120, #28299121, … |
| maximal normal subgroup of | #28299119, #28299120, #28299121, … |
| maximal quotient of | #28299136, #28299144, #28299160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19668);