Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #1865 |
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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=fg,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^52,d^b=dg,e^b=eg,h^b=h^52,d^c=dg,e^c=eg,h^c=h^521078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1865, C2×#20274986, #27385037, … |
| maximal normal subgroup of | D53×#1865, C2×#20274986, #27385037, … |
| maximal quotient of | #27278027, #27278055, #27278178, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4781);