Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C16×C53 ⋊ C2 |
| Sylow | C53 ⋊ #1331 |
110 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 45 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=d,c^2=eg,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^52,c^b=ce,e^b=eg,h^b=h^521708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1331, C2×#20272677, #27293831, … |
| maximal normal subgroup of | D53×#1331, C2×#20272677, #27293831, … |
| maximal quotient of | #27270742, #27270754, #27270860, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2472);