Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C53 ⋊ #1744 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C2×D53 |
| commutator | C2×C53 | C2×C4×C8 |
| Frattini | C22×C4 | C22×D53 |
| Fitting | C43×C53 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C43 | D53 |
| hypocenter | C53 | #1744 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C42 ◁ C43 | |
296 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,h^a=h^521744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27270618, #27270625, #27270647, … |
| maximal normal subgroup of | #27270618, #27270625, #27270647, … |
| maximal quotient of | #27274515, #27274517, #27274521, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4256);