Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3104 |
384 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 145 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=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^52,f^c=fg1078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27278942, #27278944, #27279275, … |
| maximal normal subgroup of | #27278942, #27278944, #27279275, … |
| maximal quotient of | #27384104, #27387086, #27388933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14549);