Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #106×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1339 |
114 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|a^2=d,c^2=fg,e^2=g,f^2=g,b^a=bc,c^a=ce,f^a=fg,h^a=h^30,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^52,d^c=dg,h^d=h^52202 conjugacy classes — view the full character table.
| maximal subgroup of | D53⋊#1339, C2×#20289686, #28308793, … |
| maximal normal subgroup of | D53⋊#1339, C2×#20289686, #28308793, … |
| maximal quotient of | #28298137, #28298139, #28298145, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19481);