Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ C2×#322 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×#6157 |
| commutator | C2×C53 | C2×C4×C8 |
| Frattini | C2×C4 | C22×#6157 |
| Fitting | C4×C8×C53 | C4 |
| socle | C22×C53 | C2×C42 |
| hypercenter | C4×C8 | #6157 |
| hypocenter | C53 | C2×#322 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
248 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bf,h^b=h^30,h^c=h^52,h^e=h^52496 conjugacy classes — view the full character table.
| maximal subgroup of | #28298302, #28298401, #322×#6157, … |
| maximal normal subgroup of | #28298302, #28298401, #322×#6157, … |
| maximal quotient of | C4×#16811464, D53⋊#1273, #28301454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19704);