Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #135×C53 ⋊ C4 |
| Sylow | C53 ⋊ #2145 |
224 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 62 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=e,c^2=g,d^2=f,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^30,d^b=dfg,e^b=eg,f^b=fg,h^e=h^52214 conjugacy classes — view the full character table.
| maximal subgroup of | #28310697, #28310698, #28310712, … |
| maximal normal subgroup of | #28310697, #28310698, #28310712, … |
| maximal quotient of | #28308497, #28308499, #28308506, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20830);