Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#322 ⋊ C2 |
| Sylow | C53 ⋊ #1336 |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^52,c^b=ceg,d^b=dg,e^b=eg,h^b=h^521072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1336, C2×#20272692, #27293885, … |
| maximal normal subgroup of | D53×#1336, C2×#20272692, #27293885, … |
| maximal quotient of | #27270748, #27270751, #27270754, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2487);