Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #3042 |
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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,b^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^52,d^b=dg,h^b=h^52,f^c=fg604 conjugacy classes — view the full character table.
| maximal subgroup of | #27421487, #27421488, #27431976, … |
| maximal normal subgroup of | #27421487, #27421488, #27431976, … |
| maximal quotient of | #27369312, #27369321, #27369330, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14024);