Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q16×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3285 |
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^52,d^b=de,e^b=eg,h^c=h^52,e^d=eg763 conjugacy classes — view the full character table.
| maximal subgroup of | #27540560, #27540567, #27540620, … |
| maximal normal subgroup of | #27540560, #27540567, #27540620, … |
| maximal quotient of | #27374644, #27374659, #27374674, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 16252);