Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #1815 |
264 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 264 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=f,b^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^52,e^c=eg,f^c=fg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27299844, #27299846, #27300251, … |
| maximal normal subgroup of | #27299844, #27299846, #27300251, … |
| maximal quotient of | #27276966, #27276981, #27277064, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4569);