Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #1757 |
284 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 121 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=f,c^2=e,e^2=g,b^a=bd,f^a=fg,d^b=dg,h^b=h^521084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271098, #27271099, #27271101, … |
| maximal normal subgroup of | #27271098, #27271099, #27271101, … |
| maximal quotient of | #27274620, #27274624, #27274628, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4310);