Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1392 |
158 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 38 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,d^2=g,e^2=g,b^a=bc,c^a=cf,f^a=fg,d^b=df,h^b=h^30,d^c=dg,h^e=h^52169 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20289805, #28310363, #28310367, … |
| maximal normal subgroup of | C2×#20289805, #28310363, #28310367, … |
| maximal quotient of | #28298420, #28298467, #28298470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19600);