Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C53 ⋊ C2 |
| Sylow | C53 ⋊ #1926 |
290 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,b^2=df,c^2=dg,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^52,e^c=eg1078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1926, C2×#20275342, #27386488, … |
| maximal normal subgroup of | D53×#1926, C2×#20275342, #27386488, … |
| maximal quotient of | #27282272, #27282300, #27282412, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5137);