Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#417 ⋊ C2 |
| Sylow | C53 ⋊ #1793 |
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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=f,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,d^b=dg,e^b=eg,d^c=dg,h^c=h^52604 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1793, C2×#20274672, #27383385, … |
| maximal normal subgroup of | D53×#1793, C2×#20274672, #27383385, … |
| maximal quotient of | #27275494, #27275504, #27275606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4467);