Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ #1480 |
260 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 260 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=e,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cg,d^b=df,h^b=h^521078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27275928, #27275930, #27275938, … |
| maximal normal subgroup of | #27275928, #27275930, #27275938, … |
| maximal quotient of | #27272422, #27272447, #27272464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2908);