Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C53 ⋊ #1726 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6157 |
| commutator | C2×C53 | C43 |
| Fitting | #95×C53 | C4 |
| socle | C23×C53 | C22×C4 |
| hypercenter | #95 | #6157 |
| hypocenter | C53 | #1726 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #95 | |
328 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,c^2=f,d^2=g,h^a=h^30,c^b=cg,h^d=h^52340 conjugacy classes — view the full character table.
| maximal subgroup of | #28301956, #28301960, #28301972, … |
| maximal normal subgroup of | #28301956, #28301960, #28301972, … |
| maximal quotient of | #28300037, #28300040, #28300046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20167);