Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×#117×C53 ⋊ C2 |
| Sylow | C53 ⋊ #1875 |
412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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=dfg,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^52,d^b=dg,f^b=fg1078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27276420, #27276421, D53×#1875, … |
| maximal normal subgroup of | #27276420, #27276421, D53×#1875, … |
| maximal quotient of | #27278628, #27278643, #27278860, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4832);