Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1364 |
86 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,c^2=fg,d^2=efg,f^2=g,b^a=bc,c^a=ce,h^a=h^30,c^b=cf,d^b=def,f^b=fg,h^d=h^52211 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20289733, D53⋊#1364, #28309671, … |
| maximal normal subgroup of | C2×#20289733, D53⋊#1364, #28309671, … |
| maximal quotient of | #28298221, #28298222, #28298701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19528);