Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C4×C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ #1957 |
436 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 141 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,b^2=dfg,c^2=e,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^521708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27270845, #27276157, #27276162, … |
| maximal normal subgroup of | #27270845, #27276157, #27276162, … |
| maximal quotient of | #27282868, #27282894, #27283074, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5316);