Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #131×C53 ⋊ C4 |
| Sylow | C53 ⋊ #2875 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×#6157 |
| commutator, socle | C2×C53 | C22×C42 |
| Fitting | #131×C53 | C4 |
| hypercenter | #131 | #6157 |
| hypocenter | C53 | #2875 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C4 ◁ #131 | |
556 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=f,e^2=g,b^a=bg,h^b=h^30,d^c=dg,h^f=h^52328 conjugacy classes — view the full character table.
| maximal subgroup of | #28310517, #28310518, #28318607, … |
| maximal normal subgroup of | #28310517, #28310518, #28318607, … |
| maximal quotient of | #28313766, #28313767, #28313768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21080);