Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ #1999 |
496 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^52,c^b=cf,d^b=dg,h^b=h^521072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27270764, #27270766, #27270788, … |
| maximal normal subgroup of | #27270764, #27270766, #27270788, … |
| maximal quotient of | #27284290, #27284297, #27284318, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5508);