Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#356 ⋊ C2 |
| Sylow | C53 ⋊ #2204 |
236 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^52,c^b=cg,d^b=dg,e^b=efg,h^b=h^52,d^c=df,e^c=eg,h^c=h^52,e^d=eg358 conjugacy classes — view the full character table.
| maximal subgroup of | #27304852, #27304853, #27304857, … |
| maximal normal subgroup of | #27304852, #27304853, #27304857, … |
| maximal quotient of | #27296176, #27296181, #27296344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6538);