Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×M32×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2220 |
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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=dfg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^52,c^b=cg1066 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#2220, C2×#20276828, #27538557, … |
| maximal normal subgroup of | D53×#2220, C2×#20276828, #27538557, … |
| maximal quotient of | #27298325, #27298376, #27298444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6623);