Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #2183 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D53 |
| commutator, socle | C22×C53 | C22×C8 |
| Fitting | C4×C16×C53 | C2 |
| hypercenter | C4×C16 | D53 |
| hypocenter | C53 | #2183 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C16 | |
126 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^521720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271571, #27271573, #27295863, … |
| maximal normal subgroup of | #27271571, #27271573, #27295863, … |
| maximal quotient of | #27299439, #27299446, #27301707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6418);