Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×#6157 |
| commutator, socle | C2×C53 | C22×C16 |
| Fitting | #131×C53 | C4 |
| hypercenter | #131 | #6157 |
| hypocenter | C53 | #2258 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C8 ◁ #131 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^30,c^b=cg,h^d=h^52340 conjugacy classes — view the full character table.
| maximal subgroup of | #28312637, #28312638, #28312640, … |
| maximal normal subgroup of | #28312637, #28312638, #28312640, … |
| maximal quotient of | #28312319, #28312340, #28312585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20933);