Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #1294 |
276 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 276 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=d,b^2=e,c^2=f,b^a=bc,c^a=cf,e^a=efg,h^a=h^52,c^b=cg1078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1294, C2×#20272594, #27274078, … |
| maximal normal subgroup of | D53×#1294, C2×#20272594, #27274078, … |
| maximal quotient of | #27270644, #27270651, #27270655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2389);