Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #1738 |
372 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 189 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,d^2=g,e^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^52,c^b=cg1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27289430, #27289431, #27289476, … |
| maximal normal subgroup of | #27289430, #27289431, #27289476, … |
| maximal quotient of | #27273554, #27273564, #27273568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4237);