Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #2236 |
140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 53 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=g,c^2=dg,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^52,e^c=ef,f^c=fg757 conjugacy classes — view the full character table.
| maximal subgroup of | #27297313, #27297314, #27297318, … |
| maximal normal subgroup of | #27297313, #27297314, #27297318, … |
| maximal quotient of | #27300384, #27300591, #27301040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6712);