Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C32×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C2×D53 |
| commutator, socle | C2×C53 | C22×C16 |
| Frattini | C16 | C22×D53 |
| Fitting | C2×C32×C53 | C2 |
| hypercenter | C2×C32 | D53 |
| hypocenter | C53 | #2258 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C32 ◁ C2×C32 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,d^2=e,e^2=f,f^2=g,c^b=cg,h^c=h^521744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271904, #27271906, #27304654, … |
| maximal normal subgroup of | #27271904, #27271906, #27304654, … |
| maximal quotient of | #27304270, #27304271, #27304287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6803);