Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#322 ⋊ C2 |
| Sylow | C53 ⋊ #1592 |
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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=e,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,h^a=h^52,c^b=cg,d^b=df,h^b=h^521072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1592, C2×#20273619, #27353864, … |
| maximal normal subgroup of | D53×#1592, C2×#20273619, #27353864, … |
| maximal quotient of | #27274926, #27274933, #27275346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3414);