Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3055 |
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^c=h^52604 conjugacy classes — view the full character table.
| maximal subgroup of | #27421514, #27421517, #27421536, … |
| maximal normal subgroup of | #27421514, #27421517, #27421536, … |
| maximal quotient of | #27366854, #27366876, #27366898, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14123);