Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C22⋊C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ #1516 |
284 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 73 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,d^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^52,c^b=cf,d^b=dg,e^b=efg,h^b=h^521072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27276265, #27276266, #27276269, … |
| maximal normal subgroup of | #27276265, #27276266, #27276269, … |
| maximal quotient of | #27272102, #27272107, #27272122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3067);