Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1370 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | D212 |
| commutator | C4×C53 | C2×C16 |
| Frattini | C4×C8 | C2×D53 |
| Fitting | C82×C53 | C2 |
| socle | C22×C53 | C4⋊C8 |
| hypercenter | C82 | D53 |
| hypocenter | C53 | #1370 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 ◁ C82 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=ce,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^521720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27270741, #27270742, #27270744, … |
| maximal normal subgroup of | #27270741, #27270742, #27270744, … |
| maximal quotient of | #27270832, #27270834, #27270955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2580);