Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C53 ⋊ C2 |
| Sylow | C53 ⋊ #1509 |
242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 242 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,c^2=fg,d^2=g,b^a=bd,d^a=df,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 | #27275972, #27275977, #27275979, … |
| maximal normal subgroup of | #27275972, #27275977, #27275979, … |
| maximal quotient of | #27272084, #27272097, #27272132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3033);