Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C23×C4×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1390 |
234 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 44 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,b^2=e,b^a=bc,c^a=cf,f^a=fg,h^a=h^30,d^b=df,d^c=dg,h^d=h^52442 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20289799, #28310334, #28310338, … |
| maximal normal subgroup of | C2×#20289799, #28310334, #28310338, … |
| maximal quotient of | #28298418, #28298468, #28298472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19594);