Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×M16×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3151 |
656 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|b^2=e,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^52,d^b=dg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27281618, #27281645, #27281700, … |
| maximal normal subgroup of | #27281618, #27281645, #27281700, … |
| maximal quotient of | #27371935, #27371979, #27372022, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14962);