Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #2897 |
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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,e^2=g,b^a=be,e^a=eg,h^a=h^52,e^b=eg,d^c=dg928 conjugacy classes — view the full character table.
| maximal subgroup of | #27400067, #27400074, #27400085, … |
| maximal normal subgroup of | #27400067, #27400074, #27400085, … |
| maximal quotient of | #27350474, #27350569, #27350670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13036);