Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3261 |
322 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 109 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=g,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,f^c=fg,h^c=h^52,h^d=h^52442 conjugacy classes — view the full character table.
| maximal subgroup of | #27296604, #27296607, #27297454, … |
| maximal normal subgroup of | #27296604, #27296607, #27297454, … |
| maximal quotient of | #27394085, #27394516, #27396304, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15961);