Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #2153 |
152 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 89 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=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,c^b=cg,h^b=h^521084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27300206, #27300207, #27300210, … |
| maximal normal subgroup of | #27300206, #27300207, #27300210, … |
| maximal quotient of | #27295639, #27295641, #27295665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6275);