Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1323 |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^30,c^b=cg,d^b=deg,h^b=h^52,h^d=h^52298 conjugacy classes — view the full character table.
| maximal subgroup of | D53⋊#1323, C2×#20289654, #28307954, … |
| maximal normal subgroup of | D53⋊#1323, C2×#20289654, #28307954, … |
| maximal quotient of | #28298115, #28298117, #28298119, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19449);